Question

A sample of gas ($\gamma =1.5$) is taken through an adiabatic process in which the volume is compressed from $2000{\text{cm}}^3$ to $500{\text{cm}}^3$. If the initial pressure is $120\text{kPa}$, then:

• A. The final pressure at point 2 is $960\text{kPa}$.
• B. Heat transferred, $\Delta Q_{12}=0$.
• C. Work done on the gas is $480\text{J}$.
• D. The final pressure at point 2 is $480\text{kPa}$.

Answer 1

Answer: (A), (B), (C)

The correct options are
A The final pressure at point 2 is $960\text{kPa}$.
B Heat transferred, $\Delta Q_{12}=0$.
C Work done on the gas is $480\text{J}$.

For an adiabatic process,
$P_1{V}_1^{\gamma }$ = $P_2{V}_2^{\gamma }$
[$P=\text{Pressure and}V=\text{Volume}$]
$\Rightarrow P_2=P_1(\frac{V_1}{V_2}{)}^{\gamma }=120\times (\frac{2000}{500}{)}^{1.5}=960\text{kPa}$

Work done in adiabatic process is
$W=\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}=\frac{(120\times {10}^3)(2000\times {10}^{-6})-(960\times {10}^3)(500\times {10}^{-6})}{1.5-1}=-480\text{J}$

So, work done on the gas is $480\text{J}$
Also, heat transferred in adiabatic process is always zero.
Hence, options (a), (b), (c) are correct.