Solution Found!
A piston-fitted cylinder with a 6-cm inner diameter
Chapter 7, Problem 7.11(choose chapter or problem)
A piston-fitted cylinder with a 6-cm inner diameter contains 1.40 g of nitrogen. The mass of the piston is 4.50 kg, and a 20.00-kg weight rests on the piston. The gas temperature is 30C, and the pressure outside the cylinder is 1.00 atm. 4.50 kg 1--6cm---1 (a) Prove that the absolute pressure of the gas in the cylinder is 1.86 X 105 Pa. Then calculate the volume occupied by the gas, assuming ideal gas behavior. (b) Suppose the weight is abruptly lifted and the piston rises to a new equilibrium position. Further suppose that the process takes place in two steps: a rapid step in which a negligible amount of heat is exchanged with the surroundings, followed by a slow step in which the gas returns to 30C. Considering the gas as the system, write the energy balances for step 1, step 2, and the overall process. In all cases, neglect t::.Ek and tJ.Ep If 0 varies proportionally with T, does the gas temperature increase or decrease in step 1? Briefly explain your answer. (c) The work done by the gas equals the restraining force (the weight of the piston plus the force due to atmospheric pressure) times the distance traveled by the piston. Calculate this quantity 343 and use it to determine the heat transferred to or from (state which) the surroundings during the process
Questions & Answers
QUESTION:
A piston-fitted cylinder with a 6-cm inner diameter contains 1.40 g of nitrogen. The mass of the piston is 4.50 kg, and a 20.00-kg weight rests on the piston. The gas temperature is 30C, and the pressure outside the cylinder is 1.00 atm. 4.50 kg 1--6cm---1 (a) Prove that the absolute pressure of the gas in the cylinder is 1.86 X 105 Pa. Then calculate the volume occupied by the gas, assuming ideal gas behavior. (b) Suppose the weight is abruptly lifted and the piston rises to a new equilibrium position. Further suppose that the process takes place in two steps: a rapid step in which a negligible amount of heat is exchanged with the surroundings, followed by a slow step in which the gas returns to 30C. Considering the gas as the system, write the energy balances for step 1, step 2, and the overall process. In all cases, neglect t::.Ek and tJ.Ep If 0 varies proportionally with T, does the gas temperature increase or decrease in step 1? Briefly explain your answer. (c) The work done by the gas equals the restraining force (the weight of the piston plus the force due to atmospheric pressure) times the distance traveled by the piston. Calculate this quantity 343 and use it to determine the heat transferred to or from (state which) the surroundings during the process
ANSWER:Problem 7.11
A piston-fitted cylinder with a 6-cm inner diameter contains 1.40 g of nitrogen. The mass of the piston is 4.50 kg, and a 20.00-kg weight rests on the piston. The gas temperature is 30C, and the pressure outside the cylinder is 1.00 atm. 4.50 kg 1--6cm---1 (a) Prove that the absolute pressure of the gas in the cylinder is 1.86 X 105 Pa. Then calculate the volume occupied by the gas, assuming ideal gas behavior. (b) Suppose the weight is abruptly lifted and the piston rises to a new equilibrium position. Further suppose that the process takes place in two steps: a rapid step in which a negligible amount of heat is exchanged with the surroundings, followed by a slow step in which the gas returns to 30C. Considering the gas as the system, write the energy balances for step 1, step 2, and the overall process. In all cases, neglect t::.Ek and tJ.Ep If 0 varies proportionally with T, does the gas temperature increase or decrease in step 1? Briefly explain your answer. (c) The work done by the gas equals the restraining force (the weight of the piston plus the force due to atmospheric pressure) times the distance traveled by the piston. Calculate this quantity 343 and use it to determine the heat transferred to or from (state which) the surroundings during the process.
Step by Step Solution
Step 1 of 3
a)
The force acting on the piston from the mass is equal to the gauge pressure acting on the area of the piston.
Let’s calculate the 
From the given,
The mass of piston = 4.50 kg
Weight rests on the piston = 20.00 kg
Diameter = 6cm = 0.06 m
Substitute the values in the equation (1)
The absolute pressure is then the gauge pressure plus the atmospheric pressure;
Therefore, the absolute pressure of the nitrogen gas is 
Let’s calculate the occupied volume of nitrogen gas by using the ideal gas equation.
From the given,
Mass of nitrogen = 1.40 g
Molar mass of nitrogen = 28.02 g/mol
Gas constant = 0.08206 L .atm /(mol.K)
Temperature = 273.15 + 30 = 303 .15K
Substitute the values in the ideal gas equation.
Therefore, the occupied volume of nitrogen gas is 0.677L.
___________________________________________________________________________