Question

The specific heat capacities of hydrogen at constant volume and at constant pressure 2.4 cal $g^{-1}{}^0{C}^{-1}$ and $3.4cal{g}^{-1}{}^0{C}^{-1}$ respectively. The molecular weight of hydrogen is 2 g $mo{l}^{-1}$ and the gas constant $R=8.3\times {10}^{\gamma }$ ~$er{g}^0{C}^{-1}mo{l}^{-1}.$ Calculate the valuve of J

Answer 1

$C_v\left(H_2\right)=2.4cal,/g{}^{\circ }C,$

$C_p\left(H_2\right)=3.4cal,/g{}^{\circ }C$

M = 2 g/mol.

R = 8.3 $\times {10}^{7}erg/mol{.}^{\circ }C$

We know, $C_p-C_v$ = 1 cal/g ${}^{\circ }C$

So, difference of molar specific heat,

$\Rightarrow C_p\times M-C_v\times M=1cal/g^{\circ }C$

Now, $2\times J=R$

$\Rightarrow 2\times J=8.3\times {10}_{7}erg/mol.{-}^{\circ }C$

$\Rightarrow J=4.15\times {10}_7$ erg/cal.