Correct Answer - Option 3 : 470 °C
Concept:
According to First Law of Thermodynamics:
δQ = dU + δW
For insulated room δQ = 0
∴ dU + δW = 0
∴ dU = -δW [-ve implies that work is done on the system]
Change in internal energy (dU) = mcvdT
where m = mass, cv = specific heat capacity at constant volume, dT = difference between final and initial temperature.
Calculation:
Given:
Dimension of room = 2.5 m × 3 m × 3 m, Initial temperature Ti = 20°C, Time = 24 hours ⇒ 24 × 3600 sec, ρ = 1.2 kg/m3, cv = 0.717 kJ/kg, Electric bulb heating rate = 100 W.
The work done on the room by electric heater is δW
δW = 100 × 24 × 3600 = 8.64 × 106 J
Volume of room = 2.5 × 3 × 3 = 22.5 m3
Mass of air = ρV ⇒ 1.2 × 22.5 = 27 kg.
Let T2 be the final temperature of the gas.
Because the volume of the room is constant
δW = dU
δW = mCv(T2 – T1)
8.64 × 106 = 27 × 0.717 × 103 × (T2 – 20)
T2 = 466.30° C ≈ 470°C