Thermodynamics Question 286
Question: A Carnot engine operating between temperatures $ T _{1} $ and $ T _{2} $ has efficiency$ \frac{1}{6} $ . When $ T _{2} $ is lowered by 62 K its efficiency increases to $ \frac{1}{3} $ . Then $ T _{1} $ and $ T _{2} $ are, respectively
Options:
A) 372 K and 330 K
B) 330 K and 268 K
C) 310 K and 248 K
D) 372 K and 310 K
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ {\eta _{1}}=1-\frac{T _{2}}{T _{1}}\Rightarrow \frac{1}{6}=1-\frac{T _{2}}{T _{1}}\Rightarrow \frac{T _{2}}{T _{1}}=\frac{5}{6} $ …(i)
$ {\eta _{2}}=1-\frac{T _{2}-62}{T _{1}}\Rightarrow \frac{1}{3}=1-\frac{T _{2}-62}{T _{1}} $ -(ii)
On solving Eqs. (i) and (ii) $ T _{1}=372K $ and $ T _{2}=310K $
