Thermodynamics Question 309
Question: A diesel engine takes in 5 moles of air at $ 20{}^\circ C $ and 1 atm, and compresses it adiabatically to $ \frac{1}{10}\text{th} $ of the original volume. If air is diatomic then work done and change in internal energy is
Options:
A) - 46 kJ, 46 kJ
B) 36 kJ, - 36 kJ
C) 46 kJ, - 46 kJ
D) - 36 kJ, 36 kJ
Show Answer
Answer:
Correct Answer: A
Solution:
[a]Let $ p _{1}=1 $ atm, $ n=5mol,293K $
$ V _{2}=\frac{V _{1}}{10} $
Using $ T _{1}V _{1}^{\gamma -1}=T _{2}V _{2}^{\gamma -1} $
$ \Rightarrow $ $ T _{2}=T _{1}{{( \frac{V _{1}}{V _{2}} )}^{\gamma -1}} $
$ =293{{(10)}^{0.4}}=736K $
Now, work done $ =\frac{nR(T _{1}-T _{2})}{\gamma -1} $
$ =\frac{5\times 8.3\times (293-736)}{0.4}=-46kJ $
and $ \Delta U=\Delta Q-W=0-W=46kJ $
