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Second Law of Thermodynamics

A Carnot engi...

Question

A Carnot engine absorbs an amount of Q heat from a reservoir at an absolute temperature T and rejects heat to a sink at a temperature of T/3. The amount of heat rejected is

Q/4

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Q/3

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Q/2

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2Q/3

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Solution

The correct option is D 2Q/3
By definition of Carnot Engine,
$n = \frac{W}{Q_{1}} = \frac{Q_{1} - Q_{2}}{Q_{1}} = \frac{T_{1} - T_{2}}{T_{1}}$
$\Rightarrow 1 = \frac{Q_{2}}{Q_{1}} = 1 - \frac{T_{2}}{T_{1}}$
$\frac{Q_{2}}{Q_{1}} = \frac{T_{2}}{T_{1}}$
$\frac{Q_{2}}{Q} = \frac{T / 3}{T}$
$Q_{2} = \frac{Q}{3}$
Thus amount of heat rejected as work
$W = Q_{1} - Q_{2} = Q - \frac{Q}{3} = \frac{2 Q}{3}$

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A Carnot engine absorbs an amount of Q heat from a reservoir at an absolute temperature T and rejects heat to a sink at a temperature of T/3. The amount of heat rejected is

The correct option is D 2Q/3By definition of Carnot Engine,n=WQ1=Q1−Q2Q1=T1−T2T1⇒1=Q2Q1=1−T2T1Q2Q1=T2T1Q2Q=T/3TQ2=Q3Thus amount of heat rejected as workW=Q1−Q2=Q−Q3=2Q3