Thermodynamics Question 155
Question: A Carnot engine absorbs an amount Q of heat from a reservoir at an abosolute temperature T and rejects heat to a sink at a temperature of T/3. The amount of heat rejected is
[UPSEAT 2004]
Options:
A) Q / 4
B) Q / 3
C) Q / 2
D) 2Q / 3
Show Answer
Answer:
Correct Answer: B
Solution:
$ \because \ \eta =1-\frac{T _{2}}{T _{1}}=\frac{W}{Q _{1}} $
$ T _{2}=300K $ where $ Q _{1}= $ heat absorbed, $ Q _{2}= $ heat rejected
Therefore $ 1-\frac{T/3}{T}=\frac{W}{Q _{1}} $
Therefore $ \frac{2}{3}=\frac{W}{Q _{1}}=\frac{Q _{1}-Q _{2}}{Q _{1}} $
Therefore $ \frac{2}{3}=1-\frac{Q _{2}}{Q _{1}} $
Therefore $ \frac{Q _{2}}{Q _{1}}=\frac{1}{3} $
Therefore $ Q _{2}=\frac{Q _{1}}{3}=\frac{Q}{3} $
