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Q.

A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas ( $\frac{W}{Q}$ ) is

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a

$\frac{3}{5}$

b

1

c

$\frac{2}{3}$

d

$\frac{2}{5}$

answer is A.

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Detailed Solution

Take 1 mole of gas $C_{p} ∆ T = C_{v} ∆ T + ∆ W$

$∴ ∆ W = (C_{p} - C_{v}) ∆ T$

Fraction of heat coverted into work

$\frac{∆ W}{∆ Q} = \frac{(C_{p} - C_{v}) ∆ T}{C_{p} ∆ T} = - 1 - \frac{1}{γ} = (1 - \frac{3}{5}) = \frac{2}{5}$

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