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# What amount of heat must be supplied to 2.0 × 10 ^–2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of N 2 = 28; R = 8.3 J mol^–1 K^–1 .)

Q12.2 What amount of heat must be supplied to $2.0\times 10^{-2}\ kg$ of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of $N = 28;\ R = 8.3\ J\ mol^{-1}K^{-1}$ .)

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Mass of nitrogen, $m=2.0\times 10^{-2}kg=20g$

Molar Mass of nitrogen, MN = 28 g

Number of moles is n

$\\n=\frac{m}{M_{N}}\\ n=\frac{20}{28}\\ n=0.714$

As nitrogen is a diatomic gas it's molar specific heat at constant pressure CP is as follows

$\\C_{P}=\frac{7R}{2}\\ C_{P}=\frac{7\times 8.3}{2}\\ C_{P}=29.05\ J\ mol^{-1}\ ^{o}C^{-1}$

Rise in temperature, $\\\Delta T=45 ^{o}C^{-1}$

Amount of heat Q that must be supplied is

$\\Q=nC_{P}\Delta T\\ Q=0.714\times 29.05\times 45\\ Q=933.38\ J$

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