Question

The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal g−1 °C−1 and 3.4 cal g−1 °C−1 respectively. The molecular weight of hydrogen is 2 g mol−1 and the gas constant, R = 8.3 × 107 erg °C−1 mol−1. Calculate the value of J.

Answer 1

The value of J is J=4.15×10^7 erg/cal.

Explanation:

Cv (H2)=2.4 cal/g∘C

Cp (H2)=3.4 cal./g∘C

M = 2g/Mol.

R = 8.3×10^7 erg/mol∘C

We know, Cp − Cv = 1 cal/g∘C

So, difference of molar specific heat,.

Cp×M−Cv×M=1cal/g∘C

Now, 2×J=R

2×J=8.3×10^7 erg/mol∘C

J=4.15×10^7 erg/cal.

Hence the value of J is J=4.15×10^7 erg/cal.

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Answer 2

The value of J is $4.15 \times 10^{7} \text { erg/cal}$

Explanation:

Specific heat consumption at volume constant,  $C_{v}\left(H_{2}\right)=2.4 \mathrm{cal} / \mathrm{g}-^{\circ} \mathrm{C}$

Specific calorific capacity at pressure constant,  $C_{p}\left(H_{2}\right)=3.4 \mathrm{cal} / \mathrm{g}-^{\circ} \mathrm{C}$

Molecular Strength, M = 2 g/mol

constant Gas, $R=8.3 \times 107 \mathrm{erg} / \mathrm{mol}-^{\circ} \mathrm{C}$

We know that : $c_{p}-c_{v}=1 \mathrm{cal} / \mathrm{g}-^{\circ} \mathrm{C}$

Where $C_{p} \text { and }C_{v}$ are heat capacity specific to molars.

So, the disparity in heat common to molars,

$c_{p} \times M-C_{v} \times M=1 \mathrm{cal} / \mathrm{mol}-^{\circ} \mathrm{C}$

$\begin{array}{l}\text { Now, } 2 \times J=R \\2 \times J=8.3 \times 10^{7} \text { erg/mol-oc }\end{array}$

$J=4.15 \times 10^{7} \text { erg/cal}$

Thus the value of J is $4.15 \times 10^{7} \text { erg/cal}$