Question

# The temperature outside is -10 C . You have a heat pump that can deliver 2kW...

The temperature outside is -10 C . You have a heat pump that can deliver 2kW of heat to your room. The only heat transfer occurs through a glass window which has an area of 5.1m2, a thickness of 1.3mm and a thermal conductivity of 0..8W/mK. Given that the room has no curtains, your room is otherwise well insulated and the outside temperature stays the same, what is the highest temperature that the room will reach.

We know that Heat transfer rate due to conduction is given by:

H = Q/t = k*A*dT/dx

dT = change in temperature = H*dx/(k*A)

H = Power delivered = 2 kW = 2000 W

dx = thickness of glass window = 1.3 mm = 1.3*10^-3 m

k = thermal conductivity = 0.8 W/m.K

A = Area of window = 5.1 m^2

So,

dT = 2000*1.3*10^-3/(0.8*5.1)

dT = 0.63725 C

T_in - T_out = 0.64

T_in = T_out + 0.64

T_in = max temperature inside room = -10 + 0.64

T_in = -9.36 C

Let me know if you've any query.

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