The heat energy required to raise the temperature of $5\,moles$ of an ideal gas to $5\,K$ at constant pressure is $600\,J$ . How much heat (in $J$ ) is required to raise the same mass of the same gas to $5\,K$ at constant volume ? (Take $R = 8.3\,J/mole-^oK$ )
Diffcult
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At constant pressure, heat energy required is given by
$\mathrm{Q}_{\mathrm{p}}=\mu \mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}=600 \mathrm{J}(\text { given })$
where $\mu$ is the number of moles of ideal gas. At constant volume,
$\mathrm{Q}_{\mathrm{v}}=\mu \mathrm{C}_{\mathrm{v}} \mathrm{dT}=\mu\left(\mathrm{C}_{\mathrm{p}}-\mathrm{R}\right) \Delta \mathrm{T}$
$\left(\because C_{p}-C_{v}=R\right)$
$=600-\mu R . \Delta T$
$=600-5 \times 8.31 \times 5$
$=600-207.75=392.25 \mathrm{J}$
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