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 m3. Assume (i) piston and the cylinder are insulated and (ii) air behaves as an ideal gas with Cv = 700 J/(kg.K). Find the rise in temperature of air.
Energy added by electric resistor = V I t = 12 x 1.5 x 90 = 1620 J
Work done = -ò PdV = -P(V2 - V1) = -1.2 x 105 x DV = 1.2 x 105 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 = mCVDT
DT = 420/(0.1 x 700) = 6 K.