How much heat energy in joules must be supplied to 14gms of nitrogen at room temperature to rise its temperature by $40^{o} C$ at constant pressure? (Mol.wt.of $N_{2} = 28 g m, R = c o n s t a n t$ )

50 R

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60 R

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70 R

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80 R

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Solution

The correct option is C $50 R$
Change in temp. $= △ T = T_{f} - T_{i} = 40^{\circ} C = 40 k$
$^{n} N_{2} = \frac{14}{28} = \frac{1}{2}$
Degree of freedom of $N_{2} = 5$
$△ U = \frac{f}{2} n R T_{f} - \frac{f}{2} n R T_{i} = \frac{f}{2} n R △ T$
$\Rightarrow △ U = \frac{5}{2} \times \frac{1}{2} \times R \times 40$
$△ U = 50 R$ ( In joules)

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