Question

To raise the temperature of $1$ mole of a diatomic gas by $1{}^{\circ }C$ at constant pressure, the required amount of heat is $120cal.$
The amount of heat which goes as the internal energy is almost equal to:

• A. $82.5cal$
• B. $80.2cal$
• C. $85.7cal$
• D. $58.8cal$

Answer 1

The correct option is C $85.7cal$

Given, to raise the temperature of $1$ mole of a diatomic gas by $1{}^{\circ }C$ at constant pressure, the required amount of heat is $120cal$
So heact capacity at constant pressure $C_P=120cal$
For a diatomic gas, $\frac{C_P}{C_V}=\frac{\frac{7}{2}R}{\frac{5}{2}R}=\frac{7}{5}$.
$\Rightarrow C_V=\frac{5}{7}\times 120$
Again,change in internal energy, $\Delta U=n{C}_{v}dT=\frac{5}{7}\times 120\times 1=85.71cal$