Question:
One mole of a mono-atomic ideal gas undergoes a quasi-static process, which is depicted by a straight line joining points $(V_0, T_0)$ and $(2V_0, 3T_0)$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_0, T_0)$ ?
One mole of a mono-atomic ideal gas undergoes a quasi-static process, which is depicted by a straight line joining points $(V_0, T_0)$ and $(2V_0, 3T_0)$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_0, T_0)$ ?
Updated On: Apr 26, 2024
- $R$
- $\frac{3}{2}R$
- $2R$
- $0$
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The Correct Option is C
Solution and Explanation
Heat capacity of an ideal gas in a thermodynamic process,
$\because$ Ideal gas is monoatomic,
$ C_{V} =\frac{f R}{2}=\frac{3 R}{2} $
$C_{\text {proces }} =C_{V}+\frac{p}{n} \cdot \frac{d V}{d T} $
$ \therefore =\frac{3}{2} R+\frac{p}{n} \cdot \frac{V_{0}}{2 T} $
$ \therefore C_{\text {proces }}=\frac{3}{2} R+\frac{n R T}{n 2 T} \,[\because pV = nRT]$
$=\frac{3}{2} R+\frac{R}{2}=2 R $
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Concepts Used:
Specific Heat Capacity
Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1°C.
Molar Specific Heat:
The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1°C.
Specific Heat at Constant Pressure or Volume:
The volume of solid remains constant when heated through a small range of temperature. This is known as specific heat at a constant volume. It is denoted as CV.
The pressure of solid remains constant when heated through a small range of temperature. This is known as specific heat at constant pressure which can be denoted as CP.