The specific heat of argon at constant pressu | vedclass

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(A) For an ideal gas,the relation between molar specific heats is $C_p - C_v = R$,where $R$ is the universal gas constant.Since $C_p$ and $C_v$ are gi

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$\frac{P}{T(C_p-C_v)}$

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(A) For an ideal gas,the relation between molar specific heats is $C_p - C_v = R$,where $R$ is the universal gas constant.Since $C_p$ and $C_v$ are given as specific heats (per unit mass),we use the relation $C_p - C_v = \frac{R}{M}$,where $M$ is the molar mass of the gas.Thus,$R = M(C_p - C_v)$.The ideal gas equation is $PV = nRT$,where $n = \frac{m}{M}$ is the number of moles.Substituting $n$ and $R$ into the equation: $PV = \frac{m}{M} \cdot M(C_p - C_v) \cdot T$.Simplifying,we get $PV = m(C_p - C_v)T$.Since density $\rho = \frac{m}{V}$,we can rewrite the equation as $P = \frac{m}{V}(C_p - C_v)T$.Therefore,$\rho = \frac{P}{(C_p - C_v)T}$.

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. Its density $\rho$ at $N.T.P.$ will be: [Where $P$ and $T$ are pressure and temperature respectively at $N.T.P.$]

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