A certain amount of ideal monoatomic gas undergoes a process given by $U V = K$ where $U$ is the internal energy of the gas, $V$ is volume and $K$ is a constant. The molar specific heat of the gas for the process will be

\frac{3 R}{2}

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3 R

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\frac{5 R}{2}

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\frac{R}{2}

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Solution

The correct option is D $\frac{R}{2}$
$U V = K$

$n f \frac{R T}{2} . V = K$

$T V =$ constant

$P V^{2} =$ constant

for $P V^{α} =$ constant
( $α = 2$ )

$C = C_{v} - \frac{R}{α - 1}$

$= \frac{3 R}{2} - \frac{R}{2 - 1}$

$= \frac{3 R}{2} - R = \frac{R}{2}$

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A certain amount of ideal monoatomic gas undergoes a process given by UV=K where U is the internal energy of the gas, V is volume and K is a constant. The molar specific heat of the gas for the process will be

The correct option is D R2UV=K nfRT2.V=K TV= constant PV2= constant for PVα= constant (α=2) C=Cv−Rα−1 =3R2−R2−1 =3R2−R=R2

A certain amount of ideal monoatomic gas undergoes a process given by $U V = K$ where $U$ is the internal energy of the gas, $V$ is volume and $K$ is a constant. The molar specific heat of the gas for the process will be

The correct option is D $\frac{R}{2}$
$U V = K$

$n f \frac{R T}{2} . V = K$

$T V =$ constant

$P V^{2} =$ constant

for $P V^{α} =$ constant
( $α = 2$ )

$C = C_{v} - \frac{R}{α - 1}$

$= \frac{3 R}{2} - \frac{R}{2 - 1}$

$= \frac{3 R}{2} - R = \frac{R}{2}$