When an ideal gas expands adiabatically it is observed that p∝T4. Then Cv of the gas is

PV = nRT and P=CT4∴PV=nRPC1/4⇒P3/4.V=const⇒PV4/3=const∴γ=CpCv=43∴Cv=Rγ-1=R43-1=3R

When an ideal gas expands adiabatically it is observed that p∝T4. Then Cv of the gas is

PV = nRT and P=CT4∴PV=nRPC1/4⇒P3/4.V=const⇒PV4/3=const∴γ=CpCv=43∴Cv=Rγ-1=R43-1=3R

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When an ideal gas expands adiabatically it is observed that $p \propto T^{4}$ . Then $C_{v}$ of the gas is

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$\frac{5 R}{2}$

$\frac{3 R}{2}$

answer is D.

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PV = nRT and $P = {CT}^{4}$

$∴ PV = nR {(\frac{P}{C})}^{1 / 4} \Rightarrow P^{3 / 4} . V = const \Rightarrow {PV}^{4 / 3} = const$

$∴ γ = \frac{C_{p}}{C_{v}} = \frac{4}{3}$

$∴ C_{v} = \frac{R}{γ - 1} = \frac{R}{(\frac{4}{3} - 1)} = 3 R$

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When an ideal gas expands adiabatically it is observed that p∝T4. Then Cv of the gas is

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When an ideal gas expands adiabatically it is observed that $p \propto T^{4}$ . Then $C_{v}$ of the gas is