Question

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

• A. $7.802\times {10}^{6}J$
• B. $5.232\times {10}^{6}J$
• C. $8.232\times {10}^{6}J$
• D. $7.232\times {10}^{6}J$

Answer 1

The correct option is D $7.232\times {10}^{6}J$

$K.E_1=\frac{3}{2}\frac{m_{1}R{T}_1}{M}$ …..(i)

$K.E_2=\frac{3}{2}\frac{m_{2}R{T}_2}{M}$ …..(ii)

Divide equation (ii) by (i)

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

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

$\therefore \frac{K.E_2}{K.E_1}=\frac{16}{3}$

$\therefore K.E_2=K.E_1\times \frac{16}{3}$

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

$\therefore K.E_2=7.232\times {10}^6$J.