A monoatomic gas performs a work of \(\frac Q4\) where \(Q\) is the heat supplied to it. The molar heat capacity of the gas will be ____ \(R\) during this transformation. Where \(R\) is the gas constant.
Correct Answer: 2
Solution and Explanation
According to the first law of thermodynamics,
\(Δ U = Δ Q -\frac {Δ Q}{4}\)
\(Δ U = \frac 34Δ Q\)
\(⇒ nC_vΔT = \frac 34nCΔT\)
\(⇒ C = \frac {4C_v}{3}\)
\(= 2R\)
So, the answer is \(2\).
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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.