Question

The volume of $1kg$ of hydrogen gas at $N.T.P$ is $11.2m^3$. Specific heat of hydrogen at constant volume is $10046Jk{g}^{-1}{K}^{-1}$. Find the specific heat at constant pressure.

• A. $13.8kJ/kg-K$
• B. $14.2kJ/kg-K$
• C. $16.4kJ/kg-K$
• D. $18.3kJ/kg-K$

Answer 1

The correct option is A $13.8kJ/kg-K$

Given that,

Mass of hydrogen $m=1kg$

Volume of hydrogen $V=11.2m^3$

Specific heat of hydrogen at constant volume $C_V=10046JK{g}^{-1}{k}^{-1}$

We know that,

N.T.P condition as follows

$P=1.01\times {10}^{5}N/m^2$

$T={25}^{0}C=298K$

Applying gas equation

$PV=nRT$

Putting the values in the above equation

$PV=nRT$

$1.01\times {10}^5\times 11.2=1\times R\times 298$

$R=3795.97J/kgk$

Now according to the Mayer's law

$C_P-C_V=R$

Putting the values in the above equation

$C_P-C_V=R$

$C_P=3795.97+10046$

$C_P=13841.97JK{g}^{-1}{k}^{-1}$

Hence, the specific heat of hydrogen at constant pressure is $13841.97J/Kg-k$