Question

If for an ideal gas, the ratio of pressure and volume is constant and is equal to $1 \,atm \,L ^{-1},$ the molar heat capacity at constant pressure would be

• A. $\frac{3}{2} R$
• B. $2 R$
• C. $\frac{5}{2} R$
• D. zero

Answer 1

Answer: (B)

By definition

$H=E+P V$

$\left(\frac{d H}{d T}\right)_{P}=\left(\frac{d E}{d T}\right)_{P}++P\left(\frac{d V}{d T}\right)_{P}=C_{p, m}$

For the given ideal gas, we will have $P V=R T$

or $\,\,\,\, V^{2}=R T\,\,\,\,$ or $\,\,\,\, 2 V\left(\frac{d V}{d T}\right)_{P}=R$

or $\,\,\,\,\left(\frac{d V}{d T}\right)_{P}=\frac{R}{2 V}$

$E=\frac{3 R T}{2}$

or $\left(\frac{d E}{d T}\right)_{P}=\frac{3}{2} R=C_{v, m}$

$C_{p}, m=\frac{3}{2} R+P \times \frac{R}{2 V}=\left(\frac{3}{2}+\frac{1}{2}\right) R=2 R$