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)

2 R

Answer 2

By definition

H = E + PV

$\left( \frac{dH}{dT} \right)_{P}$ = $\left( \frac{dE}{dT} \right)_{P}$+ P$\left( \frac{dV}{dT} \right)_{P}$= C_{p, m}

For the given ideal gas, we will have PV = RT

or V² = RT

or 2V $\left( \frac{dV}{dT} \right)_{P}$ = R

or $\left( \frac{dV}{dT} \right)_{P}$ = $\frac{R}{2V}$

E = $\frac{3RT}{2}$

or $\left( \frac{dE}{dT} \right)_{P}$ = $\frac{3}{2}$ R = C_v,_m

C_p , _m = $\frac{3}{2}$ R + P × $\frac{R}{2V}$= $\left( \frac{3}{2} + \frac{1}{2} \right)$ R = 2R