1 mole of gas is contained in a box of volume at T = 300 K. The gas is heated to a temperature of T= 3000 K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)
(a) same as the pressure initially
(b) 2 times the pressure initially
(c) 10 times the pressure initially
(d) 20 times the pressure initially
The answer is the option (d)
The transfer of the rate of change of momentum by the particles to the walls is what causes exertion of pressure by the gas. As temperature rises and hydrogen molecules break into atoms, the mass of the particle becomes halved, and the number of particles becomes double. Since the velocity is strictly dependent on the temperature, at the same temperature, i.e. at 300K, the velocity of particles of as well as H remains the same. Also, the pressure does not change as the atomic form changes since the rate of transfer of momentum is also same in the case of as well as H.