### Thermodynamics

# Constant Pressure Heat Addition

A vertical cylinder with a freely floating piston contains 0.1 kg air at 1.2 bar and a small electric resistor. The resistor is wired to an external 12 Volt battery. When a current of 1.5 Amps is passed through the resistor for 90 sec, the piston sweeps a volume of 0.01 m^{3}. Assume (i) piston and the cylinder are insulated and (ii) air behaves as an ideal gas with C_{v} = 700 J/(kg.K). Find the rise in temperature of air.

Calculations:

Energy added by electric resistor = V I t = 12 x 1.5 x 90 = 1620 J

Work done = -ò
PdV = -P(V_{2} - V_{1}) = -1.2 x 10^{5} x DV = 1.2 x 10^{5} x 0.01 = 1200 J

DU = Q + W = 1620 - 1200 = 420 J (energy added to the system and work added to the system are taken as positive.)

DU = mC_{V}DT

DT = 420/(0.1 x 700) = 6 K.