Question

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume ($? = 1.4$ and $2^{-1.4} = 0.38$). The ratio of the final to initial pressure is

• A. $0.76 : 1$
• B. $1 : 1$
• C. $0.66 : 1$
• D. $0.86 : 1$

Answer 1

Answer: (A)

$0.76 : 1$

Answer 2

We are given that an ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically. So we have for an adiabatic process
$p_{f} V_{f}^{\gamma}=p_{i} V_{i}^{\gamma}$
Here, $p_{i}=2 p, V_{i} =\frac{V}{2}, V_{f}=V$
So, $\frac{p_{f}}{p_{i}}=2\left(\frac{V}{2 V}\right)^{\gamma}$
$=2 \times 2^{-\gamma}=2 \times 2^{-1.4}$
$=2 \times 0.38=0.76$