Heating the inside of a box thanks to a lamp

[Rajo Yajo]

Homework Statement

The box's measurements are 277*120*195mm.
The lamp's power is 15W.
Trying to figure out how long it will take to heat the box so that it reaches a given temperature.
According to Wikipedia ρ_air=1,2kg/m³ and c_{p air}=1004J*K^-1*kg^-1

Homework Equations

ΔU=m*c_p*ΔTemperature
E=p*Δt

The Attempt at a Solution

If we suppose that the inside of the box is only air, we will have
v_air=0.277*0.120*0.195=0.0064818m³
So, m_air=v_air*ρ_air
m_air=0.00777816kg
And,
ΔU=m_air*c_{p air}*ΔTemperature
We'll have,
ΔU≈7.8ΔTemperature
And if we assume there is no energy loss,
ΔU=E
So
7.8ΔTemperature=15Δt
Thus
Δt=0.52ΔTemperature.

The time I get seems to be too short.
Thanks in advance

 

[TomHart]

I think your answer is correct. The volume is very small - a cube around 20 cm in each dimension.

 

[haruspex]

Is the box airtight?

 

[Rajo Yajo]

Thank you for replying :)

Actually, there are five little holes on the box. They allow to put temperature sensor inside the box.

Is it possible to calculate the loss of energy due to these holes?

ps: When we do the experience, it takes around 30 seconds to gain 3°C.

 

[CWatters]

If it's an incandescent lamp then most of the power is emitted as heat in the lamp itself. So you might need to allow for the heat capacity of the lamp and the fitting or wires?.

If the lamp is an LED then most (more?) of the power is emitted as light and that will be absorbed by the walls of the box. So you may need to allow for the heat capacity of the box walls. In addition some of the heat will be conducted and radiated to the outside.

Is the air in the box stirred so that the temperature recorded is representative?

 

[CWatters]

Is it possible to calculate the loss of energy due to these holes?

With difficulty. You would need to know the air flow rate into and out of the box. Easier to just seal them up.

 

[kuruman]

ps: When we do the experience, it takes around 30 seconds to gain 3°C.

Are you measuring the temperature of the air inside the box or of the box itself? What about the heat capacity of the box? Your original post asks about the box reaching "a given temperature."

 

[Rajo Yajo]

It is an incadescent lamp, but I don't know whether I should consider its heat capacity to be E=P*Δt or use the heat capacity of tungsten.

The air inside the box is not stirred.
So I guess that the majority of the heat transfert is done by convection.

We are measuring the temperature of the air inside of the box (sorry for the ambiguity).

 

[CWatters]

Pretty sure convection won't even start until the glass of the bulb is hot and convection can be quite a slow process. I would use the specific heat capacity of the glass part of the bulb. The filament gets white hot pretty quick so it's heat capacity will be very low.