# Homework Help: Heating the inside of a box thanks to a lamp

1. Mar 22, 2017

### Rajo Yajo

1. The problem statement, all variables and given/known data
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 ρair=1,2kg/m3 and cp air=1004J*K-1*kg-1

2. Relevant equations
ΔU=m*cp*ΔTemperature
E=p*Δt

3. The attempt at a solution
If we suppose that the inside of the box is only air, we will have
vair=0.277*0.120*0.195=0.0064818m3
So, mair=vairair
mair=0.00777816kg
And,
ΔU=mair*cp 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.

2. Mar 22, 2017

### TomHart

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

3. Mar 22, 2017

### haruspex

Is the box airtight?

4. Mar 23, 2017

### Rajo Yajo

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.

5. Mar 23, 2017

### 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?

6. Mar 23, 2017

### CWatters

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

7. Mar 23, 2017

### kuruman

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."

8. Mar 24, 2017

### 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).

9. Mar 24, 2017

### CWatters

Pretty sure convection wont 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.