A Carnot's engine working between 400\,{K} and 800\,{K} has a work output of 1200\,{J} per cycle. The amount of heat energy supplied to the engine from the source in each cycle is [17 Mar 2021 Shift 1]

Correct Answer is : 2400 J2400\,{J}2400J

Correct Answer is : 2400 J2400\,{J}2400J

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Thermodynamics Part 2

Section: Physics

Question : 6 of 100

Marks: +1, -0

400\,\text{K}

800\,\text{K}

1200\,\text{J}

Solution:

Efficiency of Carnot heat engine is given by

\eta = 1 - \;\frac{T_2}{T_1}

= 1 - \;\frac{Q_2}{Q_1} = \;\frac{W}{Q_1}

.....(i)

where.

W =

net work done by the gas

Q_1 =

heat absorbed by the gas,

Q_2 =

heat released by the gas,

T_1 =

temperature of hot reservoir,

and

T_2 =

temperature of cold reservoir.

Using Eq. (i), we can write

1 - \;\frac{T_2}{T_1} = \;\frac{W}{Q_1} \Rightarrow \;\frac{T_2}{T_1} = 1 - \;\frac{W}{Q_1}

\Rightarrow \;\frac{400}{800} = 1 - \;\frac{W}{Q_1} \Rightarrow \;\frac{W}{Q_1} = 1 - \;\frac{400}{800}

\Rightarrow \;\frac{W}{Q_1} = 1 - \;\frac{1}{2} = \;\frac{1}{2} \Rightarrow \;\frac{W}{Q_1} = \;\frac{1}{2}

\Rightarrow \;\; Q_1 = 2 \times W = 2 \times 1200\ [\because W_1 = 1200\,\text{J}]

= 2400\,\text{J}

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