Question

A piston-cylinder device initially contains 0.3 m³ of nitrogen gas at 350 kPa and 35 ℃. An electric heater within the device is turned on and is allowed to pass a 240W for 6 minutes. Nitrogen expands at constant pressure, and a heat loss of 3000 J occurs during the process. Determine the final temperature of the nitrogen. (Average C_P for Nitrogen is 1.039 kJ/kgK and molecular weight of Nitrogen is 28.01 kg/kmol.)

 

Answer 1

Energy balance for the process

For a closed system

At constant pressure, for expansion or compression process

U + Wb = H

So expansion work (Wb) is included but it has been converted into enthalpy.

Therefore we don't require the values of internal energies and expansion work.

Correct answer of T2 = 105°C

You just need to put the values into the energy balance equation

We = 240 J/s x 6 min x 60s/min= 86400 J = 86.4 kJ

Q out = 3000 J = 3 kJ

Gas constant

R = 8.314 J/mol·K x 1kJ/1000J x 1kmol/28.01 kg x 1000mol/kmol

R = 0.297 kPa m3 /kg K

m = (P1 x V1) / (R x T1)

= 350 kPa x 0.3 m3 / (0.297 kPa m3 /kg K x (35+273))

= 1.148 kg

Cp = 1.039 kJ/kgK

T1 = 35°C

86.4 - 3 = 83.4 = 1.148 x 1.039 x ( T2 - 35)

T2 = 105 °C