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please show all steps. 2.5 kg of nitrogen gas with an initial temperature of 300 K...

please show all steps.

2.5 kg of nitrogen gas with an initial temperature of 300 K and pressure of 100 kPa is compressed to a higher pressure. The internal energy change during this process is 70 kJ/kg. Determine the final temperature of the nitrogen. Please perform at least two iterations with average specific heats.

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Answer #1

Solution:

Using the information given,

U = nCvT = nCV[Tf - Ti]

n = m/M = 2.5*103/28.014 g/mol = 89.24 mols

Cv = 5/2R [diatomic gas] and R = 8.314,

Cv = 20.785

Ti = 300K

Substitute the values,

Tf = Ti + U/nCv

= 300 + 70*103/89.24*20.785

= 300 + 37.74

= 337.74 K.

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