A certain amount of ideal monoatomic gas undergoes, process given by $U V^{\frac{1}{2}} = C$ where U is the internal energy of the gas. The molar specific heat of the gas for the process will be (C = constant)

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The internal energy of a gas is given by U=αP, where α is constant & P is pressure. If the gas is diatomic, then molar heat capacity of the gas is

The correct option is A 5R2U=αP=nCVT⇒P∝T means volume is constant, hence Q=ΔU+W (W=0 for constant volume process) Q=nCT⇒C=CV For diatomic gas, C=5R2=CV.

The internal energy of a gas is given by $U = α P,$ where $α$ is constant & $P$ is pressure. If the gas is diatomic, then molar heat capacity of the gas is

The correct option is A $\frac{5 R}{2}$
$U = α P = n C_{V} T \Rightarrow P \propto T$
means volume is constant, hence
$Q = Δ U + W$ $(W = 0 f o r c o n s t a n t v o l u m e p r o c e s s$ )
$Q = n C T \Rightarrow C = C_{V}$
For diatomic gas, $C = \frac{5 R}{2} = C_{V} .$