Heat and Thermodynamics 5 Question 43
44. An ideal gas with pressure $p$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2 V$ and a final pressure $p _i$. If the same gas is expanded adiabatically to a volume $2 V$, the final pressure is $p _a$. The ratio of the specific heats of the gas is 1.67. The ratio $p _a / p _i$ is …… .
(1994, 2M)
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Answer:
Correct Answer: 44. 0.628
Solution:
- Under isothermal conditions, $p V=$ constant
$$ \therefore \quad\left(p _i\right)(2 V)=p V $$
$$ \Rightarrow \quad p _i=p / 2 $$
Under adiabatic conditions,
$$ p V^{\gamma}=\text { constant where } \gamma=1.67 $$
$\therefore \quad\left(p _a\right)(2 V)^{1.67}=p V^{1.67}$
$$ \Rightarrow \quad p _0=p /(2)^{1.67} $$
Therefore, the ratio $p _a / p _i=\left(2 / 2^{1.67}\right)=0.628$
