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Heat Capacity at Constant Volume

If Cv = 4.96 ...

Question

If $C_{v} = 4.96 c a l / m o l . K$ then increase in internal energy when temperature of 2 moles of this gas is increased from $340 K$ to $342 K$

27.80 c a l

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19.84 c a l

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13.90 c a l

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9.92 c a l

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Solution

The correct option is B $19.84 c a l$
Change in internal energy is equal to heat supplied at constant volume i.e ,
$△ U = q_{v} = n C_{v} △ T$
$n = 2$
$T_{2} = 342 K$
$T_{1} = 340 K$
$C_{v} = 4.96 c a l / m o l . K$
$= 2 \times 4.96 \times (342 - 340) = 19.84 c a l$

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