Question

In Mayer's relation, $C_{P}-C_{V}=R$
'$R$' stands for

• A. translational kinetic energy of 1 mol gas
• B. rotational kinetic energy of 1 mol gas
• C. vibrational kinetic energy of 1 mol gas
• D. work done to increase the temperature of 1 mol gas by one degree

Answer 1

Answer: (D)

$ PV = RT$ (For $1$ mol) ....(i)
$P\left(V + \Delta V\right)=R\left(T + 1\right)$ .... (ii)
From equation (i) and (ii),
$P\Delta V=R\Delta T$
$\Delta H=\Delta U+\Delta \left(PV\right)\left(nC\right)_{p}\Delta T=\left(nC\right)_{v}\Delta T+nR\Delta TC_{p}-C_{v}=R$