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NEET PHYSICSEasy

A Carnot engine has an efficiency of 50%50\% when its source is at a temperature 327C327^\circ \mathrm{C}. The temperature of the sink is:

A

200C200^\circ \mathrm{C}

B

27C27^\circ \mathrm{C}

C

15C15^\circ \mathrm{C}

D

100C100^\circ \mathrm{C}

Step-by-Step Solution

The efficiency of a Carnot engine is given by the formula: η=1T2T1\eta = 1 - \frac{T_2}{T_1} Where T1T_1 is the temperature of the source in Kelvin and T2T_2 is the temperature of the sink in Kelvin. Given, η=50%=0.5\eta = 50\% = 0.5 T1=327C=327+273=600 KT_1 = 327^\circ \mathrm{C} = 327 + 273 = 600 \text{ K} Substituting the values: 0.5=1T26000.5 = 1 - \frac{T_2}{600} T2600=0.5    T2=300 K\frac{T_2}{600} = 0.5 \implies T_2 = 300 \text{ K} Converting the sink temperature back to Celsius: T2=300273=27CT_2 = 300 - 273 = 27^\circ \mathrm{C}

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