Question:
A carnot engine takes 300 calories of heat at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is
A carnot engine takes 300 calories of heat at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is
Updated On: Sep 4, 2024
- 1000 K
- 750 K
- 500 K
- 250 K
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The Correct Option is D
Solution and Explanation
The efficiency of a carnot engine is given as
$\eta = 1 - \frac{T_{2}}{T_{1}} = 1 -\frac{Q_{2}}{Q_{1}} $
Where, $T_1 =$ source temperature, $T_2 =$ sink temperature
$Q_1 =$ heat extracted from source and $Q_2 =$ heat given to sink.
Here, $T_1 = 500 \,K, Q_1 = 300 \,cal$ and $Q_2 = 150 \,cal$
Now putting these values in above equation,
$ 1 - \frac{T_{2}}{500} = 1 - \frac{150}{300} $
$\Rightarrow T_{2} = 500\times \frac{150}{300} = 250\, K $
Hence, the temperature of sink is $250\, K$.
$\eta = 1 - \frac{T_{2}}{T_{1}} = 1 -\frac{Q_{2}}{Q_{1}} $
Where, $T_1 =$ source temperature, $T_2 =$ sink temperature
$Q_1 =$ heat extracted from source and $Q_2 =$ heat given to sink.
Here, $T_1 = 500 \,K, Q_1 = 300 \,cal$ and $Q_2 = 150 \,cal$
Now putting these values in above equation,
$ 1 - \frac{T_{2}}{500} = 1 - \frac{150}{300} $
$\Rightarrow T_{2} = 500\times \frac{150}{300} = 250\, K $
Hence, the temperature of sink is $250\, K$.
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Concepts Used:
Heat Transfer
What is Heat Transfer?
It is defined as the movement of heat across the border of the system due to a difference in temperature between system and its surroundings.
How is Heat Transferred?
Heat can travel from one place to another in several ways. The different modes of heat transfer include:
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