At constant volume, 4 ; mol of an ideal gas when heated from 300 … - Vidyadip

MCQ

At constant volume, $4\; mol$ of an ideal gas when heated from $300\; \mathrm{K}$ to $500\; \mathrm{K}$ changes its internal energy by $5000\; \mathrm{J}$. The molar heat capacity at constant volume is ............... $\mathrm{J\,mol}^{-1} \, \mathrm{K}^{-1}$

A
$7.25$
B
$6.75$
C
$7$
✓
$6.25$

✓

Answer

Correct option: D.

$6.25$

d
For ideal gas:

$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{V}}\left[\mathrm{T}_{2}-\mathrm{T}_{1}\right]$

$\Rightarrow \quad 5000=4 \times \mathrm{C}_{\mathrm{V}}[500-300]$

$\Rightarrow \quad \mathrm{C}_{\mathrm{v}}=\frac{5000}{800}=6.25 \mathrm{J}$ $mole$ $^{-1} \mathrm{K}^{-1}$

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