Thermodynamics Ques 32
32. At $27^{\circ} $ $C$ a gas is compressed suddenly such that its pressure becomes $(1 / 8)$ of original pressure. Final temperature will be $(\gamma=5 / 3)$
[1989]
(a) $420$ $ K$
(b) $300$ $ K$
(c) $-142^{\circ}$ $ C$
(d) $327^{\circ}$ $ C$
Show Answer
Answer:
Correct Answer: 32.(c)
Solution:
- (c) $T_1^{\gamma} P_1^{1-\gamma}=T_2^{\gamma} P_2^{1-\gamma}$
$\Rightarrow(\frac{T_2}{T_1})^{\gamma}=(\frac{P_1}{P_2})^{1-\gamma}$
$\Rightarrow T_2=T_1 \cdot(\frac{P_1}{P_2})^{\frac{1-\gamma}{\gamma}}=300 \times(8)^{-2 / 5}=142^{\circ} C$
BETA
