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

• A. Q / 4
• B. Q / 3
• C. Q / 2
• D. 2Q / 3

Answer 1

Answer: (B)

Q / 3

Answer 2

$\because \eta = 1 - \frac { T _ { 2 } } { T _ { 1 } } = \frac { W } { Q _ { 1 } }$ $T_{2} = 300K$

where $Q_{1} =$ heat absorbed, $Q_{2} =$ heat rejected

⇒ $1 - \frac{T/3}{T} = \frac{W}{Q_{1}}$ ⇒ $\frac{2}{3} = \frac{W}{Q_{1}} = \frac{Q_{1} - Q_{2}}{Q_{1}}$

⇒ $\frac{2}{3} = 1 - \frac{Q_{2}}{Q_{1}}$ ⇒ $\frac{Q_{2}}{Q_{1}} = \frac{1}{3}$ ⇒ $Q_{2} = \frac{Q_{1}}{3} = \frac{Q}{3}$