Thermodynamics Question 285
Question: A diatomic ideal gas is used in a car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32 V, the efficiency of the engine is
Options:
A) 0.5
B) 0.75
C) 0.99
D) 0.25
Show Answer
Answer:
Correct Answer: B
Solution:
[b] The efficiency of cycle is $ \eta =1-\frac{T _{2}}{T _{1}} $
For adiabatic process $ T{{V}^{\gamma -1}}= $ constant
For diatomic gas $ \gamma =\frac{7}{5} $
$ T _{1}V _{1}^{\gamma -1}=T _{2}V _{2}^{\gamma -1}\text{ }T _{1}=T _{2}{{( \frac{V _{2}}{V _{1}} )}^{\gamma -1}} $
$ T _{1}=T _{2}{{(32)}^{\frac{7}{5}-1}}=T _{2}{{(2^{5})}^{2/5}}=T _{2}\times 4 $
$ T _{1}=4T _{2} $
$ \therefore \eta =( 1-\frac{1}{4} )=\frac{3}{4}=0.75 $
