Question

The volume of $1kg$ of oxygen gas at $NTP$ is $11.2m^3$. Specific heat of oxygen at constant volume is $10046Jk{g}^{-1}{k}^{-1}$. The specific heat of oxygen at constant pressure in $Jk{g}^{-1}{k}^{-1}$ is (atmospheric pressure ${10}^{5}Pa$)

• A. $17134.6$
• B. $28131.2$
• C. $13841.97$
• D. $111013$

Answer 1

The correct option is C $13841.97$

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

$PV=mRT$

plugging the values in the above equation

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

$R=3795.97J/kg/K$

Now according to the Mayer's law

$C_P-C_V=R$

plugging the values in the above equation

$C_P-10046=3795.97$

$C_P=13841.97J/kg/K$

Hence,

option $\left(C\right)$ is correct answer.