Question

The KE of 1 kg of oxygen at 300K is 1.356 * 10⁶J . Find the KE of 4kg of oxygen at 400K

Answer 1

K.E. = 3/2nRT

1 mole of oxygen = 32 gm

Moles of oxygen in 1 kg oxygen = 1000/32 mole

Number of moles in 4 kg of oxygen = 4* 1000/32

Let 1000/32 = n

So number of mole in 1 kg oxygen = n

Number of mole in 4 kg oxygen = 4n

Let T1 = 300K and T2 = 400K

KE at 300K = 3/2*n*R*T1 = 3/2nR*300 = 450nR

KE at 400K = 3/2*4n*R*T2 = 3/2 *4n * R * 400 = 2400 nR

KE at 300K = 1.356 * 10⁶J = 450nR

nR = 1.356 * 10⁶J /450

KE at 400K = 2400 nR = 2400 * 1.356 * 10⁶J /450 = 7.232 * 10⁶ J

Answer : 7.232 * 10⁶ J