Section 16.6 Ideal-Gas Processes0.0040 mol of gas

Problem 71CP 10,000 cm3 of 200°C steam at a pressure of 20 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in cm3.

Disk brakes, such as those in your car, operate by using pressurized oil to push outward on a piston. The piston, in turn, presses brake pads against a spinning rotor or wheel, as seen in Figure CP15.72. Consider a \(15 \mathrm{~kg}\) industrial grinding wheel, \(26 \mathrm{~cm}\) in diameter, spinning at \(900 \mathrm{rpm}\). The brake pads are actuated by \(2.0\)-cm-diameter pistons, and they contact the wheel an average distance \(12 \mathrm{~cm}\) from the axis. If the coefficient of kinetic friction between the brake pad and the wheel is 0.60, what oil pressure is needed to stop the wheel in 5.0 s? Equation Transcription: Text Transcription: 15 kg 26 cm 900 rpm 2.0 cm 12 cm

Problem 70CP A diving bell is a 3.0-m-tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is 20°C. The bell is lowered into the ocean until its lower end is 100 m deep. The temperature at that depth is 10°C. a. How high does the water rise in the bell after enough time has passed for the air inside to reach thermal equilibrium? ________________ b. A compressed-air hose from the surface is used to expel all the water from the bell. What minimum air pressure is needed to do this?

A cylindrical steel pressure vessel with volume \(1.30 \mathrm{~m}^{3}\) is to be tested. The vessel is entirely filled with water, then a piston at one end of the cylinder is pushed in until the pressure inside the vessel has increased by \(2000 \mathrm{kPa}\). Suddenly, a safety plug on the top bursts. How many liters of water come out? Equation Transcription: Text Transcription: 1.30 m^3 2000 kPa

A cylinder of density \(\rho_{0}\), length \(l\), and cross-section area A floats in a liquid of density \(\rho_{\mathrm{f}}\) with its axis perpendicular to the surface. Length \(h\) of the cylinder is submerged when the cylinder floats at rest. a. Show that \(h=\left(\rho_{\mathrm{o}} / \rho_{\mathrm{f}}\right)\). b. Suppose the cylinder is distance \(y\) above its equilibrium position. Find an expression for \(\left(F_{\text {net }}\right)_{y}\), the \(y\)-component of the net force on the cylinder. Use what you know to cancel terms and write this expression as simply as possible. c. You should recognize your result of part b as a version of Hooke's law. What is the "spring constant" \(k\) ? d. If you push a floating object down and release it, it bobs up and down. So it is like a spring in the sense that it oscillates if displaced from equilibrium. Use your "spring constant" and what you know about simple harmonic motion to show that the cylinder's oscillation period is \(T=2 \pi \sqrt{\frac{h}{g}}\) e. What is the oscillation period for a 100 -m-tall iceberg \(\left(\rho_{\text {icc }}=917 \mathrm{~kg} / \mathrm{m}^{3}\right)\) in seawater? Equation Transcription: Text Transcription: rho_o l rho_f h h=(rho_o/rho_f)l y (F_net)y y-component k T=2pi sqrt h/g (rho_ice=917 kg/m^3)

A cylindrical tank of diameter \(2 R\) contains water to a depth \(d\). A small hole of diameter \(2 r\) is opened in the bottom of the tank. \(r \ll R\), so the tank drains slowly. Find an expression for the time it takes to drain the tank completely. Equation Transcription: Text Transcription: 2R d 2 r r<<R

Problem 1CQ Rank in order, from highest to lowest, the temperatures T 1 = 0 K, T 2 = 0°C, and T 3 = 0°F.

Problem 1E Section 16.1 Solids, Liquids, and Gases What volume of water has the same mass as 100 cm3 of gold?

Problem 2E Section 16.1 Solids, Liquids, and Gases The nucleus of a uranium atom has a diameter of 1.5 × 10?14 m and a mass of 4.0 × 10?25 kg. What is the density of the nucleus?

Problem 3CQ a. Is there a highest temperature at which ice can exist? If so, what is it? If not, why not? ________________ b. Is there a lowest temperature at which water vapor can exist? If so, what is it? If not, why not?

Problem 2CQ The sample in an experiment is initially at 10°C. If the sample’s temperature is doubled, what is the new temperature in °C?

Problem 3E Section 16.1 Solids, Liquids, and Gases A hollow aluminum sphere with outer diameter 10.0 cm has a mass of 690 g. What is the sphere’s inner diameter?

The cylinder in Figure Q16.4 is divided into two compartments by a frictionless piston that can slide back and forth. Is the pressure on the left side greater than, less than, or equal to the pressure on the right? Explain Figure Q16.4

Problem 4E Section 16.1 Solids, Liquids, and Gases What is the diameter of a copper sphere that has the same mass as a 10 cm × 10 cm × 10 cm cube of aluminum?

Problem 5CQ A gas is in a sealed container. By what factor does the gas pressure change if a. The volume is doubled and the temperature is tripled? b. The volume is halved and the temperature is tripled?

Problem 5E Section 16.2 Atoms and Moles How many atoms are in a 2.0 cm × 2.0 cm × 2.0 cm cube of aluminum?

Problem 6E Section 16.2 Atoms and Moles How many moles are in a 2.0 cm × 2.0 cm × 2.0 cm cube of copper?

Problem 7E Section 16.2 Atoms and Moles What is the number density of (a) aluminum and (b) lead?

Problem 8CQ a. A sample of water vapor in an enclosed cylinder has an initial pressure of 500 Pa at an initial temperature of ?0.01 °C. A piston squeezes the sample smaller and smaller, without limit. Describe what happens to the water as the squeezing progresses. ________________ b. Repeat part a if the initial temperature is 0.03°C warmer.

Problem 6CQ A gas is in a sealed container. The gas pressure is tripled and the temperature is doubled. a. What happens to the number of moles of gas in the container? ________________ b. What happens to the number density of the gas in the container?

Problem 8E Section 16.2 Atoms and Moles An element in its solid phase has mass density 1750kg/m3 and number density 4.39 × 1028atoms/m3. What is the element’s atomic mass number?

Problem 7CQ An aquanaut lives in an underwater apartment 100 m beneath the surface of the ocean. Compare the freezing and boiling points of water in the aquanaut’s apartment to their values at the surface. Are they higher, lower, or the same? Explain.

Problem 9E Section 16.2 Atoms and Moles What volume of aluminum has the same number of atoms as 10 cm3 of mercury?

Problem 9CQ A gas is in a sealed container. By what factor does the gas pressure change if: a. The volume is doubled and the temperature is tripled? ________________ b. The volume is halved and the temperature is tripled?

The temperature increases from \(300 \mathrm{~K}\) to \(1200 \mathrm{~K}\) as a gas undergoes the process shown in FIGURE Q16.11. What is the final pressure? Equation Transcription: Text Transcription: 300 K 1200 K

A gas undergoes the process shown in FIGURE Q16.10. By what factor does the temperature change? FIGURE Q16.10

A student is asked to sketch a \(p V\) diagram for a gas that goes through a cycle consisting of (a) an isobaric expansion, (b) a constant-volume reduction in temperature, and (c) an isothermal process that returns the gas to its initial state. The student draws the diagram shown in FIGURE Q16.12. What, if anything, is wrong with the student's diagram? Equation Transcription: Text Transcription: pV

Problem 11E Section 16.3 Temperature Section 16.4 Phase Changes The lowest and highest natural temperatures ever recorded on earth are ?127°F in Antarctica and 136°F in Libya. What are these temperatures in °C and in K?

Problem 10E Section 16.2 Atoms and Moles 1.0 mol of gold is shaped into a sphere. What is the sphere’s diameter?

Problem 14E Section 16.3 Temperature Section 16.4 Phase Changes What is the temperature in °F and the pressure in Pa at the triple point of (a) water and (b) carbon dioxide?

Problem 12E Section 16.3 Temperature Section 16.4 Phase Changes At what temperature does the numerical value in °F match the numerical value in °C?

Problem 13E Section 16.3 Temperature Section 16.4 Phase Changes A demented scientist creates a new temperature scale, the “Z scale.” He decides to call the boiling point of nitrogen 0°Z and the melting point of iron 1000°Z. a. What is the boiling point of water on the Z scale? ________________ b. Convert 500°Z to degrees Celsius and to kelvins.

Problem 16E Section 16.5 Ideal Gases 3.0 mol of gas at a temperature of ?120°C fills a 2.0 L container. What is the gas pressure?

Problem 15E Section 16.5 Ideal Gases A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, a. Has the mass density of the gas changed? If so, by what factor? If not, why not? ________________ b. Has the number of moles of gas changed? If so, by what factor? If not, why not?

Problem 18E Section 16.5 Ideal Gases A rigid container holds 2.0 mol of gas at a pressure of 1.0 atm and a temperature of 30°C. a. What is the container’s volume? ________________ b. What is the pressure if the temperature is raised to 130°C?

Problem 20E Section 16.5 Ideal Gases A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. a. How many moles of oxygen are in the cylinder? ________________ b. How many oxygen molecules are in the cylinder? ________________ c. What is the number density of the oxygen? ________________ d. What is the reading of a pressure gauge attached to the tank?

Problem 21E Section 16.5 Ideal Gases A 10-cm-diameter cylinder of neon gas is 30 cm long and at 30°C. The pressure gauge reads 120 psi. What is the mass density of the gas?

Problem 22E Section 16.6 Ideal-Gas Processes A gas with initial state variables p 1 V 1, and T 1 expands iso-thermally until V 2 = 2V 1. What are (a) T 2 and (b) p 2 ?

Problem 19E Section 16.5 Ideal Gases The total lung capacity of a typical adult is 5.0 L. Approxi mately 20% of the air is oxygen. At sea level and at a body temperature of 37°C, how many oxygen molecules do the lungs contain at the end of a strong inhalation?

Problem 17E Section 16.5 Ideal Gases A gas at 100°C fills volume V 0. If the pressure is held constant, what is the volume if (a) the Celsius temperature is doubled and (b) the Kelvin temperature is doubled?

A gas with initial state variables \(p_{1^{\prime}}, V_{1}\), and \(T_{1}\) is cooled in an isochoric process until \(p_{2}=\frac{1}{3} p_{1}\). What are (a) \(V_{2}\) and (b) \(T_{2}\) ? Equation Transcription: Text Transcription: p_1,V_1,T_1 p_2=1/3 p_1 V_2 T_2

Problem 24E Section 16.6 Ideal-Gas Processes A rigid sphere is submerged in boiling water in a room where the air pressure is 1.0 atm. The sphere has an open valve with its inlet just above the water level. After a long period of time has elapsed, the valve is closed. What will be the pressure inside the sphere if it is then placed in (a) a mixture of ice and water and (b) an insulated box filled with dry ice?

Problem 25E Section 16.6 Ideal-Gas Processes A rigid container holds hydrogen gas at a pressure of 3.0 atm and a temperature of 20°C. What will the pressure be if the temperature is lowered to ?20°C?

Problem 26E Section 16.6 Ideal-Gas Processes A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303°C. The air above the piston is at 1.00 atm pressure. a. What is the gas pressure inside the cylinder? ________________ b. What will the height of the piston be if the temperature is lowered to 15°C?

Problem 27E 0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes heating at constant volume to a temperature of 300°C. a. What is the final pressure of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes.

\(0.10 \mathrm{~mol}\) of argon gas is admitted to an evacuated \(50 \mathrm{~cm}^{3}\) container at \(20^{\circ} \mathrm{C}\). The gas then undergoes an isothermal expansion to a volume of \(200 \mathrm{~cm}^{3}\). a. What is the final pressure of the gas? b. Show the process on a \(p V\) diagram. Include a proper scale on both axes. Equation Transcription: Text Transcription: 0.10 mol 50 cm^3 20C 200 cm^3 pV

\(10.0040 \mathrm{~mol}\) of gas undergoes the process shown in FIGURE EX16.30. a. What type of process is this? b. What are the initial and final temperatures in \({ }^{\circ} \mathrm{C}\)? Equation Transcription: Text Transcription: 0.0040 mol ^circ C

\(0.10 \mathrm{~mol}\) of argon gas is admitted to an evacuated \(50 \mathrm{~cm}^{3}\) container at \(20^{\circ} \mathrm{C}\). The gas then undergoes an isobaric heating to a temperature of \(300^{\circ} \mathrm{C}\). a. What is the final volume of the gas? b. Show the process on a \(p V\) diagram. Include a proper scale on both axes. Equation Transcription: Text Transcription: 0.10 mol 50 cm^3 20^circC 300^circC pV

II A gas with an initial temperature of \(900^{\circ} \mathrm{C}\) undergoes the process shown in FIGURE EX16.31. a. What type of process is this? b. What is the final temperature in \({ }^{\circ} \mathrm{C}\)? c. How many moles of gas are there? Equation Transcription: Text Transcription: 900^circC ^circ C

\(0.020\) mol of gas undergoes the process shown in FIGURE EX16.32. a. What type of process is this? b. What is the final temperature in \({ }^{\circ} \mathrm{C}\)? c. What is the final volume \(V_{2}\)? Equation Transcription: Text Transcription: 0.020 mol ^circ C V_2

Problem 33P The atomic mass number of copper is A = 64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the atoms left behind are in a cubic crystal lattice. What is the smallest distance between two copper atoms?

Problem 34P An element in its solid phase forms a cubic crystal lattice (see Problem 33) with mass density 7950 kg/m3. The smallest spacing between two adjacent atoms is 0.227 nm. What is the element’s atomic mass number?

Problem 35P The molecular mass of water (H2 O) is A = 18. How many protons are there in 1.0 L of liquid water?

Problem 37P The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about 2 × 106 K. The gas pressure in the corona is about 0.03 Pa. Estimate the number density of particles in the solar corona.

Problem 36P Estimate the number density of gas molecules in the earth’s atmosphere at sea level.

Problem 39P A 6.0-cm-diameter, 10-cm-long cylinder contains 100 mg of oxygen (O2 ) at a pressure less than 1 atm. The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is 100 kPa, it takes a 184 N force to pull the cap off. What is the temperature of the gas?

Problem 38P The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0 × 10?10 mm of Hg. a. What fraction is this of atmospheric pressure? ________________ b. At T = 20°C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?

Problem 40P A nebula—a region of the galaxy where new stars are forming—contains a very tenuous gas with 100 atoms/cm3. This gas is heated to 7500 K by ultraviolet radiation from nearby stars. What is the gas pressure in atm?

Problem 41P An inflated bicycle inner tube is 2.2 cm in diameter and 200 cm in circumference. A small leak causes the gauge pressure to decrease from 110 psi to 80 psi on a day when the temperature is 20°C. What mass of air is lost? Assume the air is pure nitrogen.

Problem 42P On average, each person in the industrialized world is responsible for the emission of 10,000 kg of carbon dioxide (CO2 ) every year. This includes CO2 that you generate directly, by burning fossil fuels to operate your car or your furnace, as well as CO2 generated on your behalf by electric generating stations and manufacturing plants. CO2 is a greenhouse gas that contributes to global wanning. If you were to store your yearly CO2 emissions in a cube at STP, how long would each edge of the cube be?

Problem 43P A gas at temperature T 0 and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with three times the volume, after which the pressure is half the original pressure. What is the new temperature of the gas?

Problem 44P To determine the mass of neon contained in a rigid, 2.0 L cylinder, you vary the cylinder’s temperature while recording the reading of a pressure gauge. Your data are as follows: Temperature (°C) Pressure gauge (atm) 100 6.52 150 7.80 200 8.83 250 9.59 Use the best-fit line of an appropriate graph to determine the mass of the neon.

Problem 47P On a cool morning, when the temperature is 15°C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45°C. What pressure will your tire gauge now show?

Problem 46P An electric generating plant boils water to produce high-pressure steam. The steam spins a turbine that is connected to the generator. a. How many liters of water must be boiled to fill a 5.0 m3 boiler with 50 atm of steam at 400°C? b. The steam has dropped to 2.0 atm pressure at 150°C as it exits the turbine. How much volume does it now occupy?

Problem 48P The air temperature and pressure in a laboratory are 20°C and 1.0 atm. A 1.0 L container is open to the air. The container is then sealed and placed in a bath of boiling water. After reaching thermal equilibrium, the container is opened. How many moles of air escape?

The \(3.0\)-m-long pipe in FIGURE P16.45 is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the water's surface. What is the length \(L\) of the trapped volume of air? Equation Transcription: Text Transcription: 3.0 m L

Problem 49P A gas cylinder with a tight-fitting, movable piston contains 200 cm3 of air at 1.0 atm. It floats on the surface of a swimming pool filled with 15°Cwater. The cylinder is then pulled slowly underwater to a depth of 3.0 m. What is the volume of gas at this depth?

The mercury manometer shown in FIGURE P16.50 is attached to a gas cell. The mercury height \(h\) is \(120 \mathrm{~mm}\) when the cell is placed in an ice-water mixture. The mercury height drops to \(30 \mathrm{~mm}\) when the device is carried into an industrial freezer. What is the freezer temperature? Hint: The right tube of the manometer is much narrower than the left tube. What reasonable assumption can you make about the gas volume? Equation Transcription: Text Transcription: h 120 mm 30 mm

The U-shaped tube in FIGURE P16.51 has a total length of \(1.0 \mathrm{~m}\). It is open at one end, closed at the other, and is initially filled with air at \(20^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\) pressure. Mercury is poured slowly into the open end without letting any air escape, thus compressing the air. This is continued until the open side of the tube is completely filled with mercury. What is the length \(L\) of the column of mercury? Equation Transcription: Text Transcription: 1.0 m 20^circC 1.0 atm L

Problem 53P A compressed-air cylinder is known to fail if the pressure exceeds 110 atm. A cylinder that was filled to 25 atm at 20°C is stored in a warehouse. Unfortunately, the warehouse catches fire and the temperature reaches 950°C. Does the cylinder blow?

Problem 52P A diver 50 m deep in 10°C fresh water exhales a 1.0-cm-diameter bubble. What is the bubble’s diameter just as it reaches the surface of the lake, where the water temperature is 20°C? Hint: Assume that the air bubble is always in thermal equilibrium with the surrounding water.

Reproduce Figure P16.54 on a piece of paper. A gas starts with pressure \(p_{1}\) and volume \(V_{1}\). Show on the figure the process in which the gas undergoes an isochoric process that doubles the pressure, then an isobaric process that doubles the volume, followed by an isothermal process that doubles the volume again. Label each of the three processes. Equation Transcription: Text Transcription: p_1 V_1

\(8.0 \mathrm{~g}\) of helium gas follows the process \(1 \rightarrow 2 \rightarrow 3\) shown in FIGURE P16.56. Find the values of \(V_{1}, V_{3}, p_{2}\), and \(T_{3}\). Equation Transcription: Text Transcription: 8.0 g 1 rightarrow 2 rightarrow 3 V_1,V_3,p_2, T_3

Reproduce FIGURE P16.55 on a piece of paper. A gas starts with pressure \(p_{1}\) and volume \(V_{1}\). Show on the figure the process in which the gas undergoes an isothermal process during which the volume is halved, then an isochoric process during which the pressure is halved, followed by an isobaric process during which the volume is doubled. Label each of the three processes. Equation Transcription: Text Transcription: p_1 V_1

II FIGURE P16.57 shows two different processes by which \(1.0 \mathrm{~g}\) of nitrogen gas moves from state 1 to state 2 . The temperature of state 1 is \(25^{\circ} \mathrm{C}\). What are (a) pressure \(p_{1\) and (b) temperatures (in \({ }^{\circ} \mathrm{C}\) ) \(T_{2}, T_{3}\), and \(T_{4}\) ? Equation Transcription: Text Transcription: 1.0 g 25^circC p_1 ^circC T_2,T_3,T_4

Figure P16.58 shows two different processes by which \(80 \mathrm{~mol}\) of gas move from state 1 to state 2. The dashed line is an isotherm. a. What is the temperature of the isothermal process? b. What maximum temperature is reached along the straight-line process? Equation Transcription: Text Transcription: 80 mol

\(0.10 \mathrm{~mol}\) of gas undergoes the process \(1 \rightarrow 2\) shown in Figure P16.59. a. What are temperatures \(T_{1}\) and \(T_{2}\left(\right.\) in \(\left.{ }^{\circ} \mathrm{C}\right)\)? b. What type of process is this? c. The gas undergoes an isothermal compression from point 2 until the volume is restored to the value it had at point 1 . What is the final pressure of the gas? Equation Transcription: Text Transcription: 0.10 mol 1 rightarrow 2 T_1 T_2 ^circC

\(4.0 \mathrm{~g}\) of oxygen gas, starting at \(20^{\circ} \mathrm{C}\), follow the process \(1 \rightarrow 2\) shown in Figure \(\mathrm{P} 16.61\). What is temperature \(T_{2}\) (in \({ }^{\circ} \mathrm{C}\) )? Equation Transcription: Text Transcription: 4.0 g 20^circC 1 rightarrow 2 T_2 ^circC

\(0.0050$ mol of gas undergoes the process \(1 \rightarrow 2 \rightarrow 3\) shown in Figure P16.60. What are (a) temperature \(T_{1}\), (b) pressure \(p_{2}\), and (c) volume \(V_{3} ?\) Equation Transcription: Text Transcription: 0.0050 mol 1 rightarrow 2 rightarrow 3 T_1 p_2 V_3

Problem 62P 10 g of dry ice (solid CO2 ) is placed in a 10,000 cm3 container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which CO2 is a gas. a. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm3. ________________ b. What is the final temperature of the gas (in °C)? ________________ c. Show the process on pV diagram.

Problem 63P A container of gas at 2.0 atm pressure and 127°C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again. a. What are the final pressure and temperature of the gas? ________________ b. Show this process on a pV diagram.

Problem 64P Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. a. What is the gas volume after the expansion? ________________ b. What is the gas temperature after the expansion (in °C)? The gas pressure is then decreased at constant volume until the original temperature is reached. ________________ c. What is the gas pressure after the decrease? Finally, the gas is isothermally compressed until it returns to its initial volume. ________________ d. What is the final gas pressure? ________________ e. Show the full three-step process on a pV diagram. Use appropriate scales on both axes.

In Problems 65 through 68 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a \(p V\) diagram. c. Finish the solution of the problem. \(p_{2}=\frac{300 \mathrm{~cm}^{3}}{100 \mathrm{~cm}^{3}} \times 1 \times 2 \mathrm{~atm}\) Equation Transcription: Text Transcription: pV p_2=300 cm^3/100 cm^3 x 1 x 2 atm

In Problems 65 through 68 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a \(p V\) diagram. c. Finish the solution of the problem. \(V_{2}=\frac{(400+273) K}{(50+273) K} \times 1 \times 200 \mathrm{~cm}^{3}\) Equation Transcription: Text Transcription: pV V_2=(400+273)K/(50+273)K x 1 x 200 cm^3

In Problems 65 through 68 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a \(p V\) diagram. c. Finish the solution of the problem. \(\left(T_{2}+273\right) K=\frac{200 k P a}{500 k P a} \times 1 \times(400+273) K\) Equation Transcription: Text Transcription: pV (T_2+273)K=200 kPa/500 kPa x 1 x (400+273)K

In Problems 65 through 68 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a \(p V$ diagram. c. Finish the solution of the problem. \((2.0 \times 101,300 \mathrm{~Pa})\left(100 \times 10^{-6} \mathrm{~m}^{3}\right)=n(8.31 \mathrm{~J} / \text { molK }) T_{1}\) \(n=\frac{0.12 \mathrm{~g}}{20 \mathrm{~g} / \mathrm{mol}} T_{2}=\frac{200 \mathrm{~cm}^{3}}{100 \mathrm{~cm}^{3}} \times 1 \times T_{1}\) Equation Transcription: Text Transcription: pV (2.0 x 101, 300 Pa)(100 x 10^-6 m^3)=n(8.31 J/mol K )T_1 n=0.12 g/20 g/mol T_2 200 cm^3/100 cm^3 x1x T_1