Question

The $H$ calories of heat is required to increase the temperature of one mole of monoatomic gas from ${20}^{\circ }C$ to ${30}^{\circ }C$ at constant volume . The quantity of heat required to increase the temperature of $2$ moles of a diatomic gas from ${20}^{\circ }C$ to ${25}^{\circ }C$ is at constant volume is :

• A. $\frac{4H}{3}$
• B. $\frac{5H}{3}$
• C. $2H$
• D. $\frac{7H}{3}$

Answer 1

The correct option is B $\frac{5H}{3}$

At constant volume

$Q{=}^n{C}_v\left(△T\right)$

$H=I\times C_v\left(10\right)$

for mono atomic gas $y=\frac{5}{3}$

$C_v=\frac{R}{y-1}$

$\therefore C_v=\frac{3R}{2}$

$\therefore H=\frac{3R}{2}\times 10=15R.$

Now, no . of moles = 2

diatomic gas $\therefore y=1.4=7/5$

At constant volume

$Q{=}^n{C}_v\left(△T\right)$ ${20}^{\circ }\to {25}^{\circ }$

$=2\times \frac{R}{\frac{7}{5}-1}(25-20)$

$=2\times \frac{5R}{2}\times 5=25R.$

Required heat

$\therefore Q=25\times \frac{H}{15}$

$\because (H=15R)$

$=\frac{5H}{3}$