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Relation between Cp and Cv

Heat energy o...

Question

Heat energy of $743 J$ is needed to raise the temperature of $5$ moles of an ideal gas by $2 K$ at constant pressure. How much heat energy is needed to raise the temperature of the same mass of the gas by $2 K$ at constant volume?

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Solution

At constant pressure,
$Q_{1} =^{n} C_{P} Δ T = 743 J$
At consatnt volume,
$Q_{2} =^{n} C_{v} Δ T = n (c_{p} - R) d T$
$= 743 - 5 \times 8.3 \times 2$
$= 660 J$

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