Answer:
Final Temperature = 350.88 K = 77.88°C
Explanation:
The first law of thermodynamics in this case, can be written as:
Q + E = ΔU + W
where,
Q = heat added to system = 50 KJ
E = electrical work added to system = 80 KJ
W = Work Done by the System = 20 KJ
ΔU = Change in Internal Energy of Gas = ?
Therefore,
50 KJ + 80 KJ = ΔU + 20 KJ
ΔU = 130 KJ - 20 KJ
ΔU = 110 KJ
but, the change in internal energy of a gas is given as:
ΔU = m Cv ΔT = 110 KJ
where,
m = mass of nitrogen = 2 kg
Cv = Specific Heat at Constant Volume of Nitrogen = 1.04 KJ/kg.K
ΔT = Change in Temperature = ?
Therefore,
110 KJ = (2 kg)(1.04 KJ/kg.K)ΔT
ΔT = (110 KJ)/(2.08 KJ/K)
ΔT = 52.88 K
ΔT = Final Temperature - Initial Temperature
52.88 K = Final Temperature - 298 K
Final Temperature = 298 K + 52.88 K
Final Temperature = 350.88 K = 77.88°C
