The specific heat at constant pressure of a real gas obeying PV² = RT equation is: (a) R (b) CV + R (c) CV + R/2V (d) R/3 + CV

Answer: (c). First law at constant pressure: CP = CV + P((∂ V)/(∂ T))P (one mole). PV² = RT at constant P: 2PV dV = R dT ⇒ dV/dT = R/2PV CP = CV + P · R/2PV = CV + R/2V So the answer is (c).

The specific heat at constant pressure of a real gas obeying PV² = RT… | JEE Main 2024 (6 Apr, Shift 1)

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Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

The specific heat at constant pressure of a real gas obeying $PV^2 = RT$ equation is:

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Answer: (c)

First law at constant pressure: $C_P = C_V + P\left(\dfrac{\partial V}{\partial T}\right)_P$ (one mole).
$PV^2 = RT$ at constant $P$ : $2PV\,dV = R\,dT \Rightarrow \dfrac{dV}{dT} = \dfrac{R}{2PV}$
$C_P = C_V + P \cdot \dfrac{R}{2PV} = C_V + \dfrac{R}{2V}$
So the answer is (c).

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Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation question from JEE Main 2024 (6 Apr, Shift 1)

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