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:
- Conduction - Heat flows from things with higher temp to objects with lower temp.
- Convection - Movement of liquid molecules from higher temp regions to lower temp regions.
- Radiation - Radiant heat is present in every other way in our daily lives. Thermal radiations are also known to as radiant heat. Thermal radiation is generated by the emission of electromagnetic waves.
