Liquid nitrogen, with a boiling point of 77 K, is used as a coolant. How much energy must be removed from 1.1 kg of gaseous nitrogen at 77 K for it to completely liquefy?
Assume the latent heat of liquid nitrogen is 2.01 × 10^5 J/kg.
The liquid nitrogen has to be created at a temperature of 77 K so that it can be used as a coolant. The boiling point of nitrogen is approximately 77 K. To create the liquid nitrogen, first the temperature of any gaseous nitrogen has to be reduced to 77 K and then the latent heat of liquefaction removed to allow the change in phase from gas to liquid.
Here, the gaseous nitrogen is already given to be at 77 K. The mass of the gas is 1.1 kg. The latent heat of liquefaction is given as 2.01*10^5 J/kg. This implies that if 2.01*10^5 J of energy is extracted from one kg of gaseous nitrogen at 77 K it changes phase and is converted to liquid nitrogen at 77 K.
To convert 1.1 kg of the gas the heat to be extracted is 1.1*2.01*10^5 = 2.211*10^5 J