Question

An ideal gas is placed in a tall vertical cylinder with cross-sectional area A = 0.1 m2. A frictionless moveable piston is located vertically into the cylinder. The mass M of piston can be adjusted by adding (or subtracting) mass to it; gas pressure in the jar supports the piston’s weight.

a) Assume initial pressure of the gas is Pa = 0.022 atm and its temperature is Ta = 300 K and the piston is a height za = 1 meter above bottom of the cylinder. What is initial mass of the piston?

(b) The cylinder is now brought into thermal contact with a reservoir at temperature Tb =180 K. How high is piston above the bottom of the cylinder when the system comes to thermal equilibrium? How much work Wa ->b was done by the gas and how much heat Qa ->b was transferred into gas?

(c) As keeping gas cylinder in contact with the thermal reservoir at 180 K, slowly (so that the temperature of the gas remains constant) remove (or perhaps add, you need to figure out which) mass from the piston until the piston returns to the position in (a), z = 1m. When this process is complete, what is the pressure of the gas and what is the mass of the piston? Was work done by the gas in going from (b) to (c)? (Remember that in general the work done by the gas can be positive or negative, so be careful about signs.) Was heat transferred into or out of the gas? Examine.

(d) Starting after step (c) is completed, hold the volume of gas fixed by locking the piston in place, disconnect the cylinder from the 180 K reservoir, and put it in contact with a thermal reservoir at 300 K. describe a PV diagram of steps from (a) through (d). Assuming the gas is a monatomic gas, how much heat is transferred to the gas in going from (c) back to the starting point (a) as holding the volume fixed?