Thermodynamics Question 36
Question: At $ 27^{o}C $ a gas is suddenly compressed such that its pressure becomes $ \frac{1}{8}th $ of original pressure. Temperature of the gas will be $ (\gamma =5/3) $
[BHU 2000]
Options:
A) $ -2767.23J $
B) $ 2767.23J $
C) $ 2500J $
D) $ -2500J $
Show Answer
Answer:
Correct Answer: B
Solution:
$ W=\frac{\mu R(T _{1}-T _{2})}{(\gamma -1)}=\frac{\mu RT _{1}}{(\gamma -1)}[ 1-\frac{T _{2}}{T _{1}} ] $
$ =\frac{\mu RT _{1}}{(\gamma -1)}[ 1-{{( \frac{V _{1}}{V _{2}} )}^{\gamma -1}} ] $
$ =\frac{2\times 8.31\times 300}{( \frac{5}{3}-1 )}[ 1-{{( \frac{1}{2} )}^{\frac{5}{3}-1}} ] $
$ =+2767.23\ J $
