Thermodynamics Question 302
Question: In a Carnot engine, the temperature of reservoir is $ 927{}^\circ C $ and that of sink is$ 27{}^\circ C $ . If the work done by the engine when it transfers heat from reservoir to sink is $ 12.6\times 10^{6}J, $ the quantity of heat absorbed by the engine from the reservoir is
Options:
A) $ 16.8\times 10^{6}J $
B) $ 4\times 10^{6}J $
C) $ 7.6\times 10^{6}J $
D) $ 4.2\times 10^{6}J $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] As we know $ \eta =\frac{W}{Q _{1}}=1-\frac{T _{2}}{T _{1}} $
$ \Rightarrow \eta =1-\frac{300K}{1200K}=\frac{3}{4} $
$ \frac{3}{4}=\frac{W}{Q _{1}}\Rightarrow Q _{1}=W\times \frac{4}{3}\Rightarrow Q _{1}=12.6\times 10^{6}\times \frac{4}{3} $
$ Q _{1}=16.8\times 10^{6}J. $
