BIOLOGICAL APPLICATION During his many appearances at the

Object A has a mass that is twice the mass of object B, and object A has a specific heat that is twice the specific heat of object B. If equal amounts of heat are transferred to these objects, how do the subsequent changes in their temperatures compare?

Object Ahas a mass that is twice the mass of object B. The temperature change of object A is equal to the temperature change of object B when the objects absorb equal amounts of heat. It follows that their specific heats are related by (a) (b) (c) (d) None of the above.

The specific heat of aluminum is more than twice the specific heat of copper. Ablock of copper and a block of aluminum have the same mass and temperature The blocks are simultaneously dropped into a single calorimeter containing water at Which statement is true when thermal equilibrium is reached? (a) The aluminum block is at a higher temperature than the copper block. (b) The aluminum block has absorbed less energy than the copper block. (c) The aluminum block has absorbed more energy than the copper block. (d) Both (a) and (c) are correct statements.

A block of copper is in a pot of boiling water and has a temperature of The block is removed from the boiling water and immediately placed in an insulated container filled with a quantity of water that has a temperature of and the same mass as the block of copper. (The heat capacity of the insulated container is negligible.) The final temperature will be closest to (a) (b) (c)

You pour both a certain amount of water at and an equal amount of water at into an insulated container. The final temperature of the mixture will be (a) (b) less than (c) greater than

You pour some water at and some ice cubes at into an insulated container. The final temperature of the mixture will be (a) (b) less than but larger than (c) (d) You cannot tell the final temperature from the data given.

You pour some water at and some ice cubes at into an insulated container. When thermal equilibrium is reached, you notice some ice remains and floats in liquid water. The final temperature of the mixture is (a) above (b) less than (c) (d) You cannot tell the final temperature from the data given.

Joules experiment establishing the mechanical equivalence of heat involved the conversion of mechanical energy into internal energy. Give some everyday examples in which some of the internal energy of a system is converted into mechanical energy

Can a gas absorb heat while its internal energy does not change? If so, give an example. If not, explain why not. 1

The equation is the formal statement of the first law of thermodynamics. In this equation, the quantities and respectively, represent (a) the heat absorbed by the system and the work done by the system, (b) the heat absorbed by the system and the work done on the system, (c) the heat released by the system and the work done by the system, (d) the heat released by the system and the work done on the system.

A real gas cools during a free expansion, while an ideal gas does not cool during a free expansion. Explain the reason for this difference.

An ideal gas that has a pressure of 1.0 atm and a temperature of 300 K is confined to half of an insulated container by a thin partition. The other half of the container is a vacuum. The partition is punctured and equilibrium is quickly reestablished. Which of the following is correct? (a) The gas pressure is 0.50 atm and the temperature of the gas is 150 K. (b) The gas pressure is 1.0 atm and the temperature of the gas is 150 K. (c) The gas pressure is 0.50 atm and the temperature of the gas is 300 K. (d) None of the above

A gas consists of ions that repel each other. The gas undergoes a free expansion in which no heat is absorbed or released and no work is done. Does the temperature of the gas increase, decrease, or remain the same? Explain your answer.

Two gas-filled rubber balloons that have equal volumes are located at the bottom of a dark, cold lake. The temperature of the water decreases with increasing depth. One balloon rises rapidly and expands adiabatically as it rises. The other balloon rises more slowly and expands isothermally. The pressure in each balloon remains equal to the pressure in the water just next to the balloon. Which balloon has the larger volume when it reaches the surface of the lake? Explain your answer.

A gas changes its state quasi-statically from A to C along the paths shown in Figure 18-21. The work done by the gas is (a) greatest for path (b) least for path (c) greatest for path A S DS C, (d) The same for all three paths.

When an ideal gas undergoes an adiabatic process, (a) no work is done by the system, (b) no heat is transferred to the system, (c) the internal energy of the system remains constant, (d) the amount of heat transfer into the system equals the amount of work done by the system.

True or false: (a) When a system can go from state 1 to state 2 by several different processes, the amount of heat absorbed by the system will be the same for all processes. (b) When a system can go from state 1 to state 2 by several different processes, the amount of work done on the system will be the same for all processes. (c) When a system goes from state 1 to state 2 by several different processes, the change in the internal energy of the system will be the same for all processes. (d) The internal energy of a given amount of an ideal gas depends only on its absolute temperature. (e) A quasi-static process is one in which the system is never far from being in equilibrium. (f) For any substance that expands when heated, its is greater than its

The volume of a sample of gas remains constant while its pressure increases. (a) The internal energy of the system is unchanged. (b) The system does work. (c) The system absorbs no heat. (d) The change in internal energy must equal the heat absorbed by the system. (e) None of the above

When an ideal gas undergoes an isothermal process, (a) no work is done by the system, (b) no heat is absorbed by the system, (c) the heat absorbed by the system equals the change in the systems internal energy, (d) the heat absorbed by the system equals the work done by the system.

Consider the following series of sequential quasi-static processes that a system undergoes: (1) an adiabatic expansion, (2) an isothermal expansion, (3) an adiabatic compression, and (4) an isothermal compression that brings the system back to its original state. Sketch the series of processes on a diagram, and then sketch the series of processes on a diagram (in which volume is plotted as a function of temperature).

An ideal gas in a cylinder is at pressure and volume During a quasi-static adiabatic process, the gas is compressed until its volume has decreased to Then, in a quasi-static isothermal process, the gas is allowed to expand until its volume again has a value of What kind of process will return the system to its original state? Sketch the cycle on a graph.

Metal Ais denser than metal B. Which would you expect to have a higher heat capacity per unit massmetal A or metal B? Why?

An ideal gas undergoes a process during which and the volume of the gas decreases. Does its temperature increase, decrease, or remain the same during this process? Explain.

ENGINEERING APPLICATION, CONTEXT-RICH During the early stages of designing a modern electric generating plant, you are in charge of the team of environmental engineers. The new plant is to be located on the ocean and will use ocean water for cooling. The plant will produce electrical power at the rate of 1.00 GW. Because P1V _ constant SSM the plant will have an efficiency of one-third (typical of most modern plants), heat will be released to the cooling water at the rate of 2.00 GW. If environmental codes require that only water with a temperature increase of or less can be returned to the ocean, estimate the flow rate of cooling water through the plant.

A typical microwave oven has a power consumption of about 1200 W. Estimate how long it should take to boil a cup of water in the microwave, assuming that 50 percent of the electrical power consumption goes into heating the water. How does this estimate correspond to everyday experience?

A demonstration of the heating of a gas under adiabatic compression involves putting a small strip of paper into a large glass test tube, which is then sealed with a piston. If the piston compresses the trapped air very rapidly, the paper will catch fire. Assuming that the burning point of paper is estimate the factor by which the volume of the air trapped by the piston must be reduced for this demonstration to work.

A small change in the volume of a liquid occurs when heating the liquid at constant pressure. Use the following data to estimate the fractional contribution this change makes to the heat capacity of water between and The density of water at and 1.00 atm pressure is The density of liquid water at and 1.00 atm pressure is

ENGINEERING APPLICATION, CONTEXT-RICH You designed a solar home that contains of concrete How much heat is released by the concrete at night when it cools from to

How much heat must be absorbed by 60.0 g of ice at to transform it into 60.0 g of liquid water at

How much heat must be released by 0.100 kg of steam at to transform it into 0.100 kg of ice at

A 50.0-g piece of aluminum at is cooled to by placing it in a large container of liquid nitrogen at that temperature. How much nitrogen is vaporized? (Assume that the specific heat of aluminum is constant over this temperature range.)

ENGINEERING APPLICATION, CONTEXT-RICH You are supervising the creation of some lead castings for use in the construction industry. Each casting involves one of your workers pouring 0.500 kg of molten lead that has a temperature of into a cavity in a large block of ice at How much liquid water should you plan on draining per hour if there are 100 workers who are able to each average one casting every 10.0 min?

ENGINEERING APPLICATION, CONTEXT-RICH While spending the summer on your uncles horse farm, you spend a week apprenticing with his farrier (a person who makes and fits horseshoes). You observe the way he cools a shoe after pounding the hot, pliable shoe into the correct size and shape. Suppose a 750-g iron horseshoe is taken from the farriers fire, shaped, and at a temperature of dropped into a 25.0-L bucket of water at What is the final temperature of the water after the horseshoe and water arrive at equilibrium? Neglect any heating of the bucket and assume the specific heat of iron is 460 J>(kg # K). SSM

The specific heat of a certain metal can be determined by measuring the temperature change that occurs when a piece of the metal is heated and then placed in an insulated container that is made of the same material and contains water. Suppose the piece of metal has a mass of 100 g and is initially at The container has a mass of 200 g and contains 500 g of water at an initial temperature of The final temperature is What is the specific heat of the metal?

BIOLOGICAL APPLICATION During his many appearances at the Tour de France, champion bicyclist Lance Armstrong typically expended an average power of 400 W, 5.0 hours a day for 20 days. What quantity of water, initially at could be brought to a boil if you could harness all of that energy?

A25.0-g glass tumbler contains 200 mL of water at If two 15.0-g ice cubes, each at a temperature of are dropped into the tumbler, what is the final temperature of the drink? Neglect any heat transfer between the tumbler and the room.

A 200-g piece of ice at is placed in 500 g of water at This system is in a container of negligible heat capacity and is insulated from its surroundings. (a) What is the final equilibrium temperature of the system? (b) How much of the ice melts?

A 3.5-kg block of copper at a temperature of is dropped into a bucket containing a mixture of ice and water whose total mass is 1.2 kg. When thermal equilibrium is reached, the temperature of the water is How much ice was in the bucket before the copper block was placed in it? (Assume that the heat capacity of the bucket is negligible.)

A well-insulated bucket of negligible heat capacity contains 150 g of ice at (a) If 20 g of steam at is injected into the bucket, what is the final equilibrium temperature of the system? (b) Is any ice left after the system reaches equilibrium?

A calorimeter of negligible heat capacity contains 1.00 kg of water at 303 K and 50.0 g of ice at 273 K. (a) Find the final temperature T. (b) Find the final temperature T if the mass of ice is 500 g.

A 200-g aluminum calorimeter contains 600 g of water at A 100-g piece of ice cooled to is placed in the calorimeter. (a) Find the final temperature of the system, assuming no heat is transferred to or from the system. (b) A 200-g piece of ice at is added. How much ice remains in the system after the system reaches equilibrium? (c) Would the answer for Part (b) change if both pieces of ice were added at the same time?

The specific heat of a 100-g block of a substance is to be determined. The block is placed in a 25-g copper calorimeter holding 60 g of water at Then, 120 mL of water at are added to the calorimeter. When thermal equilibrium is reached, the temperature of the system is Determine the specific heat of the block.

A 100-g piece of copper is heated in a furnace to a temperature The copper is then inserted into a 150-g copper calorimeter containing 200 g of water. The initial temperature of the water and calorimeter is and the temperature after equilibrium is established is When the calorimeter and its contents are weighed, 1.20 g of water are found to have evaporated. What was the temperature t SSM C?

A 200-g aluminum calorimeter contains 500 g of water at . Aluminum shot with a mass equal to 300 g is heated to and is then placed in the calorimeter. Find the final temperature of the system, assuming that there is no heat transfer to the surroundings.

A diatomic gas does 300 J of work and also absorbs 2.50 kJ of heat. What is the change in internal energy of the gas? 4

If a gas absorbs 1.67 MJ of heat while doing 800 kJ of work, what is the change in the internal energy of the gas?

If a gas absorbs 84 J of heat while doing 30 J of work, what is the change in the internal energy of the gas?

A lead bullet initially at just melts upon striking a target. Assuming that all of the initial kinetic energy of the bullet goes into the internal energy of the bullet, calculate the impact speed of the bullet.

During a cold day, you can warm your hands by rubbing them together. Assume the coefficient of kinetic friction between your hands is 0.500, the normal force between your hands is 35.0 N, and that you rub them together at an average relative speed of (a) What is the rate at which mechanical energy is dissipated? (b) Assume further that the mass of each of your hands is 350 g, the specific heat of your hands is and that all the dissipated mechanical energy goes into increasing the temperature of your hands. How long must you rub your hands together to produce a increase in their temperature?

The gas is allowed to expand at constant pressure until it reaches its final volume. It is then cooled at constant volume until it reaches its final pressure. (a) Illustrate this process on a diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.

The gas is first cooled at constant volume until it reaches its final pressure. It is then allowed to expand at constant pressure until it reaches its final volume. (a) Illustrate this process on a PV diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.

The gas is allowed to expand isothermally until it reaches its final volume and its pressure is 1.00 atm. It is then heated at constant volume until it reaches its final pressure. (a) Illustrate this process on a diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.

The gas is heated and is allowed to expand such that it follows a single straight-line path on a diagram from its initial state to its final state. (a) Illustrate this process on a diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.

In this problem, 1.00 mol of a dilute gas initially has a pressure equal to a volume equal to and an internal energy equal to As the gas is slowly heated, the plot of its state on a diagram moves in a straight line to the final state. The gas now has a pressure equal to a volume equal to and an internal energy equal to Find the work done and the heat absorbed by the gas.

In this problem, \(1.00 \mathrm{~mol}\) of the ideal gas is heated while its volume changes, so that \(T=A P^2\), where A is a constant. The temperature changes from \(T_0\) to \(4 T_0\). Find the work done by the gas.

ENGINEERING APPLICATION, CONTEXT-RICH A sealed, almost-empty spray paint can still contains a residual amount of the propellant: 0.020 mol of nitrogen gas. The cans warning label clearly states: Do Not Dispose by Incineration. (a) Explain this warning and draw the diagram for the gas if, in fact, the can is subject to a high temperature. (b) You are in charge of testing the can. The manufacturer claims it can withstand an internal gas pressure of 6.00 atm before it breaks. The can is initially at roomtemperature and standard pressure in your testing laboratory. You begin to heat it uniformly using a heating element that has a power output of 200 W. The can and element are in an insulating oven, and you can assume of the heat released by the heating element is absorbed by the gas in the can. How long should you expect the heating element to remain on before the can bursts?

An ideal gas initially at and 200 kPa has a volume of 4.00 L. It undergoes a quasi-static, isothermal expansion until its pressure is reduced to 100 kPa. Find (a) the work done by the gas, and (b) the heat absorbed by the gas during the expansion.

The heat capacity at constant volume of a certain amount of a monatomic gas is 49.8 J/K. (a) Find the number of moles of the gas. (b) What is the internal energy of the gas at T = 300 K? (c) What is the heat capacity at constant pressure of the gas?

The heat capacity at constant pressure of a certain amount of a diatomic gas is (a) Find the number of moles of the gas. (b) What is the internal energy of the gas at (c) What is the molar heat capacity of this gas at constant volume? (d) What is the heat capacity of this gas at constant volume?

(a) Calculate the heat capacity per unit mass of air at constant volume and the heat capacity per unit mass of air at constant pressure. Assume that air has a temperature of 300 K and a pressure of Also, assume that air is composed of 74.0 percent molecules (molecular weight and 26.0 percent molecules (molar mass of and that both components are ideal gases. (b) Compare your answer for the specific heat at constant pressure to the value listed in the Handbook of Chemistry and Physics of

In this problem, 1.00 mol of an ideal diatomic gas is heated at constant volume from 300 K to 600 K. (a) Find the increase in the internal energy of the gas, the work done by the gas, and the heat absorbed by the gas. (b) Find the same quantities if this gas is heated from 300 K to 600 K at constant pressure. Use the first law of thermodynamics and your results for Part (a) to calculate the work done by the gas. (c) Again calculate the work done in Part (b). This time calculate it by integrating the equation

A diatomic gas is confined to a closed container of constant volume and at a pressure The gas is heated until its pressure triples. What amount of heat had to be absorbed by the gas in order to triple the pressure?

In this problem, 1.00 mol of air is confined in a cylinder with a piston. The confined air is maintained at a constant pressure of 1.00 atm. The air is initially at and has volume Find the volume after 13,200 J of heat are absorbed by the trapped air.

The heat capacity at constant pressure of a sample of a gas is greater than the heat capacity at constant volume by (a) How many moles of the gas are present? (b) If the gas is monatomic, what are and (c) What are the values of and at normal room temperatures?

Carbon dioxide at a pressure of 1.00 atm and a temperature of sublimates directly from a solid to a gaseous state without going through a liquid phase. What is the change in the heat capacity at constant pressure per mole of when it undergoes sublimation? (Assume that the gas molecules can rotate but do not vibrate.) Is the change in the heat capacity positive or negative during sublimation? The molecule is pictured in Figure 18-22. SSM

In this problem, 1.00 mol of a monatomic ideal gas is initially at 273 K and 1.00 atm. (a) What is the initial internal energy of the gas? (b) Find the work done by the gas when 500 J of heat are absorbed by the gas at constant pressure. What is the final internal energy of the gas? (c) Find the work done by the gas when 500 J of heat are absorbed by the gas at constant volume. What is the final internal energy of the gas?

List all of the degrees of freedom possible for a water molecule and estimate the heat capacity of water at a temperature very far above its boiling point. (Ignore the fact the molecule might dissociate at high temperatures.) Think carefully about all of the different ways in which a water molecule can vibrate.

The DulongPetit law was originally used to determine the molar mass of a substance from its measured heat capacity. The specific heat of a certain solid substance is measured to be (a) Find the molar mass of the substance. (b) What element has this specific-heat value?

A 0.500-mol sample of an ideal monatomic gas at 400 kPa and 300 K, expands quasi-statically until the pressure decreases to 160 kPa. Find the final temperature and volume of the gas, the work done by the gas, and the heat absorbed by the gas if the expansion is (a) isothermal, and (b) adiabatic.

A 0.500-mol sample of an ideal diatomic gas at \(400 \mathrm{kPa}\) and \(300 \mathrm{~K}\) expands quasi-statically until the pressure decreases to \(160 \mathrm{kPa}\). Find the final temperature and volume of the gas, the work done by the gas, and the heat absorbed by the gas if the expansion is (a) isothermal, and (b) adiabatic.

A 0.500-mol sample of helium gas expands adiabatically and quasi-statically from an initial pressure of 5.00 atm and temperature of 500 K to a final pressure of 1.00 atm. Find (a) the final temperature of the gas, (b) the final volume of the gas, (c) the work done by the gas, and (d) the change in the internal energy of the gas.

A 1.00-mol sample of gas at and 5.00 atm is allowed to expand adiabatically and quasi-statically until its pressure equals 1.00 atm. It is then heated at constant pressure until its temperature is again After it reaches a temperature of it is heated at constant volume until its pressure is again 5.00 atm. It is then compressed at constant pressure until it is back to its original state. (a) Construct a diagram showing each process in the cycle. (b) From your graph, determine the work done by the gas during the complete cycle. (c) How much heat is absorbed (or released) by the gas during the complete cycle?

A1.00-mol sample of an ideal diatomic gas is allowed to expand. This expansion is represented by the straight line from 1 to 2 in the diagram (Figure 18-23). The gas is then compressed isothermally. This compression is represented by the curved line from 2 to 1 in the diagram. Calculate the work per cycle done by the gas. SSM

A 2.00-mol sample of an ideal monatomic gas has an initial pressure of and an initial volume of The gas is taken through the following quasi-static cycle: It is expanded isothermally until it has a volume of Next, it is heated at constant volume until it has a pressure of It is then cooled at constant pressure until it is back to its initial state. (a) Show this cycle on a diagram. (b) Find the temperature at the end of each part of the cycle. (c) Calculate the heat absorbed and the work done by the gas during each part of the cycle.

At point D in Figure 18-24, the pressure and temperature of 2.00 mol of an ideal monatomic gas are 2.00 atm and 360 K, respectively. The volume of the gas at point B on the diagram is three times that at point D and its pressure is twice that at point C. Paths AB and CD represent isothermal processes. The gas is carried through a complete cycle along the path DABCD. Determine the total amount of work done by the gas and the heat absorbed by the gas along each portion of the cycle. SSM 7

At point D in Figure 18-24, the pressure and temperature of 2.00 mol of an ideal diatomic gas are 2.00 atm and 360 K, respectively. The volume of the gas at point B on the diagram is three times that at point D and its pressure is twice that at point C. Paths AB and CD represent isothermal processes. The gas is carried through a complete cycle along the path DABCD. Determine the total amount of work done by the gas and the heat absorbed by the gas along each portion of the cycle.

Asample consisting of n moles of an ideal gas is initially at pressure volume and temperature It expands isothermally until its pressure and volume are and It then expands adiabatically until its temperature is and its pressure and volume are and It is then compressed isothermally until it is at a pressure and a volume which is related to its initial volume by The gas is then compressed adiabatically until it is back in its original state. (a) Assuming that each process is quasi-static, plot this cycle on a diagram. (This cycle is known as the Carnot cycle for an ideal gas.) (b) Show that the heat absorbed during the isothermal expansion at is (c) Show that the heat released by the gas during the isothermal compression at is (d) Using the result that is constant for a quasi-static adiabatic expansion, show that (e) The efficiency of a Carnot cycle is defined as the net work done by the gas, divided by the heat absorbed by the gas. Using the first law of thermodynamics, show that the efficiency is (f) Using your results from the previous parts of this problem, show that Qc >Qh _ Tc >Th .

During the process of quasi-statically compressing an ideal diatomic gas to one-fifth of its initial volume, 180 kJ of work are done on the gas. (a) If this compression is accomplished isothermally at room temperature (293 K), how much heat is released by the gas? (b) How many moles of gas are in this sample?

The diagram in Figure 18-25 represents 3.00 mol of an ideal monatomic gas. The gas is initially at point A. The paths AD and BC represent isothermal changes. If the system is brought to point C along the path AEC, find (a) the initial and final temperatures of the gas, (b) the work done by the gas, and (c) the heat absorbed by the gas. SSM

The diagram in Figure 18-25 represents 3.00 mol of an ideal monatomic gas. The gas is initially at point A. The paths AD and BC represent isothermal changes. If the system is brought to point C along the path ABC, find (a) the initial and final temperatures of the gas, (b) the work done by the gas, and (c) the heat absorbed by the gas.

The diagram in Figure 18-25 represents 3.00 mol of an ideal monatomic gas. The gas is initially at point A. The paths AD and BC represent isothermal changes. If the system is brought to point C along the path ADC, find (a) the initial and final temperatures of the gas, (b) the work done by the gas, and (c) the heat absorbed by the gas.

Suppose that the paths AD and BC in Figure 18-25 represent adiabatic processes. What are the work done by the ga s and the heat absorbed by the gas in following the path ABC?

BIOLOGICAL APPLICATION, CONTEXT-RICH As part of a laboratory experiment, you test the calorie content of various foods. Assume that when you eat these foods, of the energy released by the foods is absorbed by your body. Suppose you burn a 2.50-g potato chip, and the resulting flame warms a small aluminum can of water. After burning the potato chip, you measure its mass to be 2.20 g. The mass of the can is 25.0 g, and the volume of water contained in the can is 15.0 mL. If the temperature increase in the water is how many kilocalories per 150-g serving of these potato chips would you estimate there are? Assume the can of water captures 50.0 percent of the heat released during the burning of the potato chip. Note: Although the joule is the SI unit of choice in most thermodynamic situations, the food industry in the United States currently expresses the energy released during metabolism in terms of the dietary calorie, which is our kilocalorie. SSM

ENGINEERING APPLICATION Diesel engines operate without spark plugs, unlike gasoline engines. The cycle that diesel engines undergo involves adiabatically compressing the air in a cylinder, and then fuel is injected. When the fuel is injected, if the air temperature inside the cylinder is above the fuels flashpoint, the fuel-air mixture will ignite. Most diesel engines have compression ratios in the range from 14:1 to 25:1. For this range of compression ratios (which are the ratio of maximum to minimum volume), what is the range of maximum temperatures of the air in the cylinder, assuming the air is taken into the cylinder at Most modern gasoline engines typically have compression ratios on the order of 8:1. Explain why you expect the diesel engine to require a better (more efficient) cooling system than its gasoline counterpart.

At very low temperatures, the specific heat of a metal is given by For copper, and (a) What is the specific heat of copper at 4.00 K? (b) How much heat is required to heat copper from 1.00 to 3.00 K?

How much work must be done on 30.0 g of carbon monoxide (CO) at standard temperature and pressure to compress it to onefifth of its initial volume if the process is (a) isothermal, (b) adiabatic?

How much work must be done on 30.0 g of carbon dioxide at standard temperature and pressure to compress it to onefifth of its initial volume if the process is (a) isothermal, (b) adiabatic?

How much work must be done on 30.0 g of argon (Ar) at standard temperature and pressure to compress it to one-fifth of its initial volume if the process is (a) isothermal, (b) adiabatic?

Athermally insulated system consists of 1.00 mol of a diatomic gas at 100 K and 2.00 mol of a solid at 200 K that are separated by a rigid insulating wall. Find the equilibrium temperature of the system after the insulating wall is removed, assuming that the gas obeys the ideal-gas law and that the solid obeys the DulongPetit law.

When an ideal gas undergoes a temperature change at constant volume, its internal energy change is given by the formula However, this formula correctly gives the change in internal energy whether the volume remains constant or not. (a) Explain why this formula gives correct results for an ideal gas even when the volume changes. (b) Using this formula, along with the first law of thermodynamics, show that for an ideal gas

An insulated cylinder is fitted with an insulated movable piston to maintain constant pressure. The cylinder initially contains 100 g of ice at Heat is transferred to the ice at a constant rate by a 100-W heater. Make a graph showing the temperature of the as a function of time starting at when the temperature is and ending at when the temperature is

(a) In this problem, 2.00 mol of a diatomic ideal gas expands adiabatically and quasi-statically. The initial temperature of the gas is 300 K. The work done by the gas during the expansion is 3.50 kJ. What is the final temperature of the gas? (b) Compare your result to the result you would get if the gas were monatomic.

A vertical insulated cylinder is divided into two parts by a movable piston of mass The piston is initially held at rest. The top part of the cylinder is evacuated and the bottom part is filled with 1.00 mol of diatomic ideal gas at temperature 300 K. After the piston is released and the system comes to equilibrium, the volume occupied by gas is halved. Find the final temperature of the gas.

According to the Einstein model of a crystalline solid, the internal energy per mole is given by where is a characteristic temperature called the Einstein temperature, and is the temperature of the solid in kelvins. Use this expression to show that a crystalline solids molar heat capacity at constant volume is given by

(a) Use the results of Problem 94 to show that in the limit that the Einstein model gives the same expression for specific heat that the Dulong-Petit law does. (b) For diamond, is approximately 1060 K. Integrate numerically to find the increase in the internal energy if 1.00 mol of diamond is heated from 300 K to 600 K

Use the results of the Einstein model in Problem 94 to determine the molar internal energy of diamond at 300 K and 600 K, and thereby the increase in internal energy as diamond is heated from 300 K to 600 K. Compare your result to that of Problem 95.

During an isothermal expansion, an ideal gas at an initial pressure expands until its volume is twice its initial volume (a) Find its pressure after the expansion. (b) The gas is then compressed adiabatically and quasi-statically until its volume is and its pressure is 1.32 Is the gas monatomic, diatomic, or polyatomic? (c) How does the translational kinetic energy of the gas change in each stage of this process?

If a hole is punctured in a tire, the gas inside will gradually leak out. Assume the following: The area of the hole is the tire volume is and the time, it takes for most of the air to leak out of the tire can be expressed in terms of the ratio the temperature the Boltzmann constant and the initial mass m of the gas inside the tire. (a) Based on these assumptions, use dimensional analysis to find an estimate for (b) Use the result of Part (a) to estimate the time it takes for a car tire with a nail hole punched in it to go flat.