Thermodynamics Question 349
Question: An ideal gas at $ 27^{o}C $ is compressed adiabatically to $ \frac{8}{27} $ of its original volume. If $ \gamma =\frac{5}{3} $ , then the rise in temperature is
Options:
A) 450 K
B) 375 K
C) 225 K
D) 405 K
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \frac{T _{2}}{T _{1}}={{( \frac{V _{1}}{V _{2}} )}^{\gamma -1}}\Rightarrow T _{2}=300{{( \frac{27}{8} )}^{\frac{5}{3}-1}}=300{{( \frac{27}{8} )}^{\frac{2}{3}}} $
$ =300{{{ {{( \frac{27}{8} )}^{1/3}} }}^{2}}=800{{( \frac{3}{2} )}^{2}}=675K $
$ \Rightarrow \ \Delta T=675-300=375\ K $
