n moles of an ideal gas with constant volume | vedclass

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(A) For an isobaric process,the work done $W$ is given by $W = P \Delta V = nR \Delta T$.The heat supplied $Q$ at constant pressure is given by $Q = n

Vedclass · Accepted Answer

$\frac{nR}{C_v + nR}$

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(A) For an isobaric process,the work done $W$ is given by $W = P \Delta V = nR \Delta T$.The heat supplied $Q$ at constant pressure is given by $Q = n C_p \Delta T$.Using Mayer's relation,$C_p = C_v + R$ (where $C_v$ and $C_p$ are molar heat capacities).Therefore,the heat supplied is $Q = n(C_v + R) \Delta T = (n C_v + nR) \Delta T$.The ratio of work done to heat supplied is $\frac{W}{Q} = \frac{nR \Delta T}{(n C_v + nR) \Delta T} = \frac{nR}{n C_v + nR}$.If $C_v$ is the total heat capacity of $n$ moles,then $C_v(	ext{total}) = n C_v(	ext{molar})$. Thus,the ratio is $\frac{nR}{C_v + nR}$.

$n$ moles of an ideal gas with constant volume heat capacity $C_v$ undergo an isobaric expansion by a certain volume. The ratio of the work done in the process to the heat supplied is

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