Heater power keeping a room constantly warm from low temperatures outside

[Karma1412]

Homework Statement

The temperature of a room in winter is kept constant at 24 °C by using a heater. The room is separated from the outside, where the temperature is -5.0 °C, by a wall of area 12 m^2 and thickness 0.20 m. The material of the wall has a thermal conductivity of 0.15 W m1 K-1. Estimate the power of the heater.

Relevant Equations

None given, and I can't find any that work or figure out how to use any

I've been trying for 45 minutes and doing research but I can't even find a start to how to approach this. :(

[Mentor Note: New user reminded to always show their work on schoolwork problems. That work is shown in a subsequent post below]

 

[Karma1412]

I've tried to do the following:
P = AM
M = eoT^4 (e being the emmisivity, o being the constant i think stefen boltzmann)
M = ((Pm^-1)/(oT^4)) x oT^4 (subbing e because emissivity = (power radiated per unit area)/(σT^4)
oT^4 x M = Pm^-1 x oT^4
M = Pm^-1 (cancelling)
and then I have no clue what to do, or if this even makes any sense or if I am using the right formula.
I have also used
Q= (ΔT⋅A⋅k)/d
to calculate
Q=(29 x 0.15)/0.20m
Q= 52.2 / 0.20
Q=261 W
but again I really dont know if what I did is real, ai generated this formula and when I searched for it online I couldn't find it.

 

[erobz]

Homework Statement: The temperature of a room in winter is kept constant at 24 °C by using a heater. The room is separated from the outside, where the temperature is -5.0 °C, by a wall of area 12 m2 and thickness 0.20 m. The material of the wall has a thermal conductivity of 0.15 W m1 K-1. Estimate the power of the heater.
Relevant Equations: I'm not sure, but the one's I've found from the research I did seem to be:
Q= (ΔT⋅A⋅k)/d (Im not sure if this formula is real, it's what ChatGPT gave me when I asked for help)
L = σAT^4 (I don't know if it is relevant)
P = AM

I've tried to do the following:
P = AM
M = eoT^4 (e being the emmisivity, o being the constant i think stefen boltzmann)
M = ((Pm^-1)/(oT^4)) x oT^4 (subbing e because emissivity = (power radiated per unit area)/(σT^4)
oT^4 x M = Pm^-1 x oT^4
M = Pm^-1 (cancelling)
and then I have no clue what to do, or if this even makes any sense or if I am using the right formula.
I have also used
Q= (ΔT⋅A⋅k)/d
to calculate
Q=(29 x 0.15)/0.20m
Q= 52.2 / 0.20
Q=261 W
but again I really dont know if what I did is real, ai generated this formula and when I searched for it online I couldn't find it.

The intention is 1D steady state thermal heat conduction through a plane wall.

 

[Karma1412]

The intention is 1D steady state thermal heat conduction through a plane wall.

thank you, ill do some research on it :)

 

[haruspex]

Homework Statement: … thermal conductivity …

which I googled and immediately found:
https://en.wikipedia.org/wiki/Thermal_conductivity_and_resistivity

 

[haruspex]

Q= (ΔT⋅A⋅k)/d

Q=(29 x 0.15)/0.20m

What about A?

 

[Nugatory]

Homework Statement: The temperature of a room in winter is kept constant at 24 °C by using a heater. The room is separated from the outside, where the temperature is -5.0 °C, by a wall of area 12 m^2 and thickness 0.20 m. The material of the wall has a thermal conductivity of 0.15 W m1 K-1. Estimate the power of the heater.
Relevant Equations: None given, and I can't find any that work or figure out how to use any

I've been trying for 45 minutes and doing research but I can't even find a start to how to approach this. :(

The temperature of the room is constant. That tells us something about the relationship between heat leaving the room and heat being added to the room.

How does heat leave the room?

How is heat added to the room?

 

[Lnewqban]

I've tried to do the following:
P = AM
M = eoT^4 (e being the emmisivity, o being the constant i think stefen boltzmann)
M = ((Pm^-1)/(oT^4)) x oT^4 (subbing e because emissivity = (power radiated per unit area)/(σT^4)
oT^4 x M = Pm^-1 x oT^4
M = Pm^-1 (cancelling)

This problem is not related to emissivity or radiation.
It is a thermal conduction one.
Energy in form of heat naturally flows through that wall from the warm to the cold space.

Please, see:
https://en.wikipedia.org/wiki/Thermal_conduction#Fourier's_law

https://en.wikipedia.org/wiki/Rate_of_heat_flow

 

[phyzguy]

What about A?

A is the wall area, given in the problem as 12 m^2.

 

[haruspex]

A is the wall area, given in the problem as 12 m^2.

I was asking why it does not appear in the second of the two equations I quoted.