Question

A rocket is propelled by a gas which is initially at a temperature of $4000K$ . The temperature of the gas falls $1000K$ as it leaves the exhaust nozzle. The gas which will acquire the largest momentum while leaving the nozzle is
A. Hydrogen
B. Helium
C. Nitrogen
D. Argon

Answer 1

Hint:When the rocket engines operate, they are continuously ejecting burned fuel gases that consist of both mass and velocity Or momentum. By the conservation law of momentum, the rocket gets momentum in the forward direction making it move forward. The escaping gases have a large mass and high speed.





Complete answer:
Generally, a rocket operates on the principle of conservation of momentum. The rocket ejects gases continuously in the backward direction which creates a momentum of the gases backward and thus the rocket gets momentum in the forward direction making it forward. Mainly the rocket operates by burning the fuel it carries and ejecting the burned exhaust gases. If the burning rate of fuel is constant then the velocity at which exhaust is ejected remains unchanged.
Therefore, the operation of a rocket depends upon the momentum of the exhausting gases. The term momentum is defined by the product of the mass and velocity of the body.
Momentum = (Mass of the body $\times $ velocity)
The higher the mass or the velocity of the body, the higher will be its momentum.
 Hydrogen, Helium, Nitrogen, and Argon have atomic numbers $1,2,7$ and $18$respectively. Therefore Argon is the heaviest gas among the four gases given in the option. Therefore, Argon gas will acquire the largest momentum while leaving the nozzle.
Thus, option (D) is correct.








Note:Currently fuels used in the rocket are liquid hydrogen and liquid oxygen which are mixed and ignited in the combustion chamber of the rocket engine. These fuels are kept at a low temperature as a liquid to increase the amount that could be carried.