Thermodynamics - Result Question 28
29. An ideal gas at $27^{\circ} C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. The rise in temperature is $(\gamma=\frac{5}{3})$
[1999]
(a) $475^{\circ} C$
(b) $402^{\circ} C$
(c) $275^{\circ} C$
(d) $175^{\circ} C$
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Answer:
Correct Answer: 29. (b)
Solution:
- (b) $T=27^{\circ} C=300 K$
$\gamma=\frac{5}{3} ; \quad V_2=\frac{8}{27} V_1 ; \quad \frac{V_1}{V_2}=\frac{27}{8}$
From adiabatic process we know that
$ T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1} $
$\frac{T_2}{T_1}=(\frac{V_1}{V_2})^{\gamma-1}=(\frac{27}{8})^{\frac{5}{3}-1}$
$\frac{T_2}{T_1}=\frac{9}{4} \Rightarrow T_2=\frac{9}{4} \times T_1=\frac{9}{4} \times 300=675 K$
$T_2=675-273^{\circ} C=402^{\circ} C$
