Question

If the temperature of 1 mole of an ideal gas is increased by ${50}^{\circ }\text{C}$, calculate the change in the kinetic energy of the system.

• A. $62.32\text{J}$
• B. $6.235\text{J}$
• C. $623.5\text{J}$
• D. $6235.0\text{J}$

Answer 1

The correct option is C $623.5\text{J}$

Kinetic energy of 1 mole of gas $\left(KE\right)=\frac{3}{2}RT$, where $R$ is the gas constant and $T$ is the temperature of gas.
Consider the initial temperature of gas to be $t{}^{\circ }C$. On heating, the final temperature of gas will be $t+50{}^{\circ }C$.
The change in the kinetic energy of the particles on heating: $\left(\Delta KE\right)=\frac{3}{2}R(t+273+50)-\frac{3}{2}R(t+273)$
$=\frac{3}{2}R\times 50$
$\Rightarrow \frac{3}{2}\times 8.314\times 50$
$=623.55\text{J}$