Hi! I need help with this assignment. Could you please be detailed with your ide

Question

Hi! I need help with this assignment. Could you please be detailed with your ideas on how to solve it? Thanks.

Consider your room/apartment/house as a closed system and make an energy balance for it for a certain time period (1 or 2 hours) by using First Law of Thermodynamics. Based on the energy balance estimate how much heat transfer you need to add or take from the system to keep the temperature constant. Estimate heat rate out of the system. Estimate power of heater which can increase your home temperature for 5 degree in 15 minutes based on the energy analysis you did.

Explanation / Answer

Let us assume a 6 m*6 m*6 m cubic room made of cement brick wall with thickness of 10 cm.

let outside temperature be 0 degree celcius and inside room temperature desired is 20 degree celcius.

assuming a cement wall, thermal conductivity=k=0.72

heat transfer per unit time=k*A*dT/dx

where A=cross sectional area=6*6

=36 m^2

dT=temperature difference=20 degrees

dx=thickness=10 cm=0.1 m

then heat requried per second=0.72*36*20/0.1

=5184 J/s

heat transfer needed for maintaing constant temperature for 1 hour=5184*3600 seconds

=1.866*10^7 J

heat rate of the system=5184 J/s

power of the heater =heat rate of the system

=5184 J/s

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