Prove that ${{C}_{p}}$ is greater than ${{C}_{v}}$

cbse
thermo-dynamics

#1

Out of the two specific heats of a gas,
Cp > Cv 1
This can be understood as follows :
In case ${{C}{v}}$ volume of the gas is kept constant and heat is required only for raising the temperature of gas through 1°C or 1K. No heat whatsoever is spent in expansion of the gas.
In case of ${{C}
{p}}$ as pressure of the gas is kept constant and the gas could expand on heating.
Some heat is spent in expansion of the gas against external pressure.
Hence, more heat is required to raise the
temperature of 1 gm mole of the gas through 1°C or 1K when heated at constant pressure.
Hence
${{C}{p}}$>${{C}{v}}$