Chapter 4.5, Problem 162FEP

A piston–cylinder device contains an ideal gas. The gas undergoes two successive cooling processes by rejecting heat to the surroundings. First the gas is cooled at constant pressure until $T_2=\frac{3}{4}{T}_1$. Then the piston is held stationary while the gas is further cooled to $T_3=\frac{1}{2}{T}_1$, where all temperatures are in K.

1. The ratio of the final volume to the initial volume of the gas is

1. (a)   0.25
2. (b)   0.50
3. (c)   0.67
4. (d)   0.75
5. (e)   1.0

2. The work done on the gas by the piston is

1. (a)   RT₁/4
2. (b)   c_vT₁/2
3. (c)   c_pT₁/2
4. (d)   (c_v + c_p)T₁/4
5. (e)   c_v(T₁ + T₂)/2

3. The total heat transferred from the gas is

1. (a)   RT₁/4
2. (b)   c_vT₁/2
3. (c)   c_pT₁/2
4. (d)   (c_v + c_p)T₁/4
5. (e)   c_v(T₁ + T₃)/2