Nitrogen gas at T29815 K and P10 bar is contained in a suppl

Nitrogen gas at T=298.15 K and P=10 bar is contained in a supply lined connected to a closed tank containing a liquid-vapor nitrogen mixture at the same pressure and at lower temperature. At the beginning, the tank contains 10 mol of liquid nitrogen, which occupies 10% of its total volume. The tank is refrigerated and, as a result, the nitrogen flows from the supply line into the tank until liquid nitrogen occupies 90% of the total tank volume at P=10 bar. Assuming that nitrogen is an ideal gas, find the total amount of heat extracted from the tank.

Solution

Given that the tank contains 10 mol of liquid nitrogen in the beginning. We know that for liquid nitrogen, the volume of 1kg liquid is 1.237 liters.

We know that the molar weight of nitrogen is 28 gms. Hence, the weight of 10 moles of nitrogen is 280 grams = 0.28kg. Hence, volume of nitrogen is 0.35 liters

Now, we know that 10% of the total volume of the tank is Nitrogen which occupies 0.35 liters. Hence, the total volume of the tank is 3.5 liters

It is given that the final result is liqid nitrogen occupying 90% of the total volume of the tank. Hence, the final volume of liquid nitrogen in the tank is 90%*3.5 = ^{3.15 liters}

We know that the initial volume of the tank is 0.35 m³. Hence, the additional nitrogen supplied is 28 liters which is 80 moles

The weight of 80 moles of Nitrogen is 80*28 = 2240 grams

We know that the specific enthalpy of Nitrogen gas entering the chamber under the given conditions is h = 460.3 J/gm

Hence, the total enthalpy of Nitrogen entering is 460.3*2240 = 1031.072 kJ

At 10 bar, the enthalpy of saturated liquid nitrogen is 87.1 J/gm

Hence, for the final stage fo the process where the entered mass of nitrogen is liquid, the total enthalpy is given by 87.1*2240 = 195.104 kJ

We know that for the nitrogen gas to be converted into saturated liquid, the enthalpy of nitrogen is reduced to saturated level. We know the initial enthalpy and the final enthalpy. The amount of heat taken out is the difference between them.

Hence, the amount of heat taken out of the liquid is 1031.072 - 195.104 = 835.97 kJ