A vertical cylinder with a freely floating piston contains

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A vertical cylinder with a freely floating piston contains 0.1 kg air at 1.2 bar and a small electrical resistor. The resistor of is wired to an external 12 volt battery. When a current of 1.5 amps is passed through the resistor for 90 secs, 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/kgK,
Find the rise in temperature of air.

1. 1
2. 2
3. 3
4. 4
5. not defined

Correct Option: E

m = 0.1 kg , P = 1.2 bar , Voltage E = 12 volt I = 1.5 A , t = 90 sec ∆v = 0.01/m³ , C_v = 700 J/kg–K
Insulated condition δq = 0
δq = δw + ∆U
0 = mCv∆T + δw_air - δw_e

∆T =	δw_air - δw_e
	mC_v

∆T =	1.2 × 10⁵ × 0.01 - 12 × 1.5 × 90
	0.1 × 700