Thermodynamics Question 316
Question: Two carnots engines A and B are operated in series. The first one A receives heat at 1200 K and rejects to a reservoir at T and K. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 300 K. Calculate the value of T, when work outputs of the two engines are equal.
Options:
A) 600 K
B) 750 K
C) 450 K
D) 900 K
Show Answer
Answer:
Correct Answer: B
Solution:
[b]$ \frac{W}{Q _{1}+W}={\eta _{1}} $
$ \frac{W}{Q _{1}}={\eta _{2}} $
$ \frac{W}{Q _{1}}=1-\frac{300}{T} $
$ \Rightarrow $ $ \frac{1}{1+\frac{T}{T-300}}=\frac{1200-T}{1200} $
$ \Rightarrow $ $ (T-300)1200=(1200-T)(2T-300) $
$ T=750K $
