Question

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.

Answer #1

**Solution:**

Using the information given,

U
= nC_{v}T
= nC_{V}[T_{f} - T_{i}]

n = m/M = 2.5*10^{3}/28.014 g/mol = 89.24 mols

C_{v} = 5/2R [diatomic gas] and R = 8.314,

C_{v} = 20.785

T_{i} = 300K

Substitute the values,

T_{f} = T_{i} +
U/nC_{v}

= 300 + 70*10^{3}/89.24*20.785

= 300 + 37.74

= **337.74 K.**

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