A piston-cylinder device initially contains 0.5m3 of nitrogen gas at 400 kPa and 27 °C. Anelectric heater within the device is turned on and is allowed to pass a current of 2 A for 5min from a 120V source. Nitrogen expands at constant pressure, and a heat loss of 2800 Joccurs during the process. Determine the final temperature of nitrogen. Assume nitrogen to be an ideal gas with M = 28 g/mol and cp=1.039 kJ/kg. K

The final temperature of nitrogen is 56.968° C.

Explanation:

Given data:

v = 0.5

P = 400 k Pa

T = 27+273 = 300 K

= 1.039 KJ/Kg K

= 2800

J = 2.8 KJ

M = 28 g/mol

Solution:

Electric work () = VI Δt

= 120V × 2A × (5×60s)(1/1000)

= 72 KJ

m =

=

= 2.245 Kg

Equation for energy balance is

- = ΔE system

- - = ΔU

- = ΔH

= m ( - )

= m ( - )

(72 - 2.8) KJ = 2.245 × 1.039 ( - 27°C)

69.2 = 2.3325 ( - 27°C)

( - 27°C) = 29.968

= 56.968° C

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