Question

A piston cylinder device contains 2 kg of nitrogen gas at 100 kPa and 25 C. We introduce 50 kJ of heat into the system as well as 80 kJ of electrical work. The system expands and produces 20 kJ of work due to such expansion. Find the final temperature of nitrogen in Celsius. Assume constant specific heats at room temperature (300 K).

Answer 1

The final temperature of nitrogen can be found using the first law of thermodynamics, considering the heat added, electrical work done on the gas, and the work done by the gas in expansion.

Step-by-step explanation:

To find the final temperature of nitrogen after adding heat and work to the system, we must understand the first law of thermodynamics, which describes how energy is conserved in a closed system. The first law is given by the equation ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. Given that nitrogen has a mass of 2 kg and the heat (Q) added is 50 kJ, electrical work (We) done on the gas is 80 kJ, and the expansion work (W) done by the gas is 20 kJ, we can calculate for the change in internal energy (ΔU) and thus the final temperature.

The net work done on the gas is the electrical work minus the expansion work, i.e., Wnet = We - W. Therefore, using the first law and assuming constant specific heats (Cp and Cv) at room temperature conditions, ΔU can be expressed as the sum of the heat added and the net work done on the gas: ΔU = Q + Wnet. Since ΔU=Cv*m*ΔT for an ideal gas, where m is the mass and ΔT is the change in temperature, we can find ΔT and hence the final temperature.

Answer 2

Final Temperature = 350.88 K = 77.88°C

Step-by-step 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