A 1.5 kW heater is to be used to heat a room with dimensions 3.5 m Times 5.0 m T

Question

A 1.5 kW heater is to be used to heat a room with dimensions 3.5 m Times 5.0 m Times 3.0 m. There are no heat losses from the room, but the room is not airtight, 3. so the pressure in the room is always atmospheric. Consider the air in the room to be an ideal gas with C^*_p = 29 J/(mol K), and its initial temperature is 10 degree C. Assuming that the rate of heat transfer from the air to the walls is low, what will be the rate of increase of the temperature in the room when the heater is turned on? What would be the rate of increase in the room temperature if the room were hermetically sealed?

Explanation / Answer

The room´s volume is V = 3.5 m x 5.0 m x 3.0 m = 48 m3

There is a 1.5 kW heater, it is equal to 5400 kJ

The air is consider an ideal gas,

Then à PV = nRT ---> n = (PV) / (RT) ---> n = (1 atm x 48000 L) / (0.082 (L.atm/K.mol) x 283.15 K)

n = 2067.33 mol of air

The initial temperature is 10°C = 283.15 K

Knowing that Q = n x Cp x T ---> T = Q / (n x Cp) ---> T= 5400000 J / (2067.33 mol x 29 (J/mol.K))

T = 90.07 K

Then, T = T2 – T1 ---> T2 = T + T1 ---> T2 = 90.07 K + 283.15 K ---> T2 = 373.22 K = 100.07°C

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