Question

A Carnot engine takes$3 \times 10^{6}cal$.Of heat from a reservoir at 627°C, and gives it to a sink at 27°C. The work done by the engine is

• A. $4.2 \times 10^{6}J$
• B. $8.4 \times 10^{6}J$
• C. $16.8 \times 10^{6}J$
• D. Zero

Answer 1

Answer: (B)

$8.4 \times 10^{6}J$

Answer 2

$\eta = 1 - \frac{T_{2}}{T_{1}} = \frac{W}{Q}$⇒$W = \left( 1 - \frac{T_{1}}{T_{2}} \right)\mspace{6mu} Q = \left\{ 1 - \frac{(273 + 27)}{(273 + 627)} \right\}$

⇒$W = \left( 1 - \frac{300}{900} \right) \times 3 \times 10^{6} = 2 \times 10^{6} \times 4.2\mspace{6mu} J = 8.4 \times 10^{6}J$