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First Law of Thermodynamics

One mole of a...

Question

One mole of an ideal gas requires $207 J$ heat to raise the temperature by $10 K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 K$ , the heat required is

A

198.7 J

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B

29 J

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C

215.3 J

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D

124 J

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Solution

The correct option is C $124 J$
When 1 mole of ideal gas is heated at constant pressure
$d Q = n C_{p} d T_{1} = n C_{v} d T_{1} + n R d T_{1}$
$207 = C_{v} (10) + R (10)$ ( $n = 1$ )
$C_{v} = 20.7 - 8.314 = 12.386 J / m o l - K$
Amount of heat required when the gas is heated at constant volume,
$d Q = d U = n C_{v} d T_{2}$
$d Q = 12.386 (10) = 123.86 J$
Option D.

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