Question

The kinetic energy of $1kg$ of oxygen at $300K$ is $1.356\times {10}^{6}J$. Find the kinetic energy of $4kg$ of oxygen at $400K$.

Answer 1

Given:Let $m_1$ be the mass of oxygen$=1$kg

and $T_1$ be the kinetic energy$=300$K

K.E is $E_1=1.356\times {10}^6$J

Let $m_2$ be the mass of oxygen$=4$kg

and $T_2$ be the kinetic energy$=400$K

To find:K.E is $E_2$

K.E$E=\frac{3m}{2M}RT$

$E_1=\frac{3m_1}{2M}R{T}_1$ ......$\left(1\right)$

$E_2=\frac{3m_2}{2M}R{T}_2$ ......$\left(2\right)$

$\frac{E_2}{E_1}=\frac{m_2}{m_1}.\frac{T_2}{T_1}$

$=\frac{4\times 400}{1\times 300}=\frac{16}{3}$

$E_2=E_1\times \frac{16}{3}$

$=1.356\times {10}^6\times \frac{16}{3}=7.232\times {10}^6$J