Heat and Thermodynamics 5 Question 42
43. A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T _i$ (in kelvin) and the final temperature is $a T _i$, the value of $a$ is
(2010)
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Answer:
Correct Answer: 43. $T$
Solution:
- In adiabatic process,
$$ \begin{aligned} T V^{\gamma-1} & =\text { constant } \\ \therefore \quad T _i V _i^{0.4} & =T _f V _f^{0.4} \quad(\text { as } \gamma=1.4 \text { for diatomic gas }) \\ \text { or } \quad T _i V _i^{0.4} & =\left(q T _i\right)\left(\frac{V _i}{32}\right)^{0.4} \\ \text { or } \quad q(32)^{0.4} & =4 \end{aligned} $$
$\therefore$ The correct answer is 4 .
