Answer to Question #150532 in Electrical Engineering for warda

Question

1kg of air enclosed in a rigid container is initially at 4.8 bar and 150 °C. The container is heated until the temperature is 200 °C. Calculate the pressure of the air finally and the heat supplied during the process

Answer 1

Given data

Mass of air = 1 kg

Initial temperature T1 = 150 + 273 = 423 K

Initial pressure P1 = 4.8 bar

Final temperature T2 = 200 + 273 = 473 K

The container is rigid (volume is constant)

From the ideal gas equation

$\frac{P1V1}{T1} = \frac{P2V2}{T2}$

$P2 = P1\times \frac{T2}{T1}$

$= 4.8 bar x (\frac{473}{423})$

= 5.37 bar

For isochoric process

Entropy change $S = Cv ln(\frac{T2}{T1})$

$= 0.718 kJ/kgK \times ln (\frac{473}{423})$

= 0.08 kJ/kgK

Average temperature T = $\frac{(473 + 423)}{2} = 448 K$

Heat supplied = $T \times S$

$= 448 K x 0.08 kJ/kgK = 35.9 kJ/kg$