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Second Law of Thermodynamics

A Carnot engi...

Question

A Carnot engine takes 100 calories of heat from a reservoir at 427C and performs 60 K of work. Calculate the amount of heat absorbed in joule

A

10 J

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B

20J

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C

68J

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D

None of the above

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Solution

The correct option is D None of the above
Given:
Heat from the reservoir, $Q_{1} = 100 c a l$
Work done, $W = 60 K c a l$
Reservoir Temperature, $T_{1} = 427 ° C = (427 + 273) K = 700 K$
To find:
Amount of heat absorbed in joule, $Q_{2} = ?$
We know the work done can be written as,
$W = Q_{1} - Q_{2} ⟹ Q_{2} = Q_{1} - W = 100 - 60000 = - 59.9 K c a l$
We know $1 c a l = 4.184 J$
$⟹ Q_{2} = - (59.9 K \times 4.184) J = - 250.621 K J$
Hence it doesn't match any of the given options.

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