Nitrogen is contained in a one m^3 rigid tank with the initial pressure and temp
ID: 1003816 • Letter: N
Question
Nitrogen is contained in a one m^3 rigid tank with the initial pressure and temperature of 10 bar and 300 K respectively. Heat transfer to the contents of the tank occurs until the temperature has increased to 400 K. During the process, a pressure relief valve allows nitrogen to escape, maintaining constant pressure in the tank. The surrounding temperature of the tank is 306 K. The nitrogen is assumed as an ideal gas during the process and it emits at the average temperature of the initial state and final state of the tank. Determine the following by stating the assumptions made, The mass of nitrogen that escapes. The amount of heat transfer. The entropy generation.Explanation / Answer
Initial temperature T1 of N2 = 300K
Pressure P of N2 = 10bar = 10 x 105pascal =constant
Volume of rigid tank = 1m3= 1000L
Surrounding temperature of tank =306K
Final temperature T2= 400K
a.The mass of N2 that escape
From Charles Law
V1/T1 = V2/T2
V2 = V1 xT2/T1= 1000L x 400K/300K =333.33L
At STP = 22.4 liters of gas is 1 mole
333.33 liters of gas is 14.88 moles
1mole of N2 = 14g/mole
14.88 moles of N2 = 14g/mole x 14.88 moles =208.33g
The mass of N2 that escape is 208.33g
b.Amount of heat transfer.
q = -w
w = - P dV =-10 x 105 0.333m2 =- 333000J =-333kJ
q = 333kJ
c.The entropy generation
At constant pressure
s = q/T = 333kJ/mole/100K = 3.33kJ/mole
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