Thermodynamics question.?

Question

You have a box. If you know the dimensions of the box, the temperature of the atmosphere around the box, and the thermodynamics properties of the box (thermal conductivity etc.), how would you find the temperature inside the box?

Note: A thermometer is NOT allowed.

Answer 1

If the thermal conductivity of the box is high (e.g. metal) then the time frame to reach equilibrium with the surrounding atmosphere is fairly short - simply wait, and see what the surrounding atmosphere does - if it is stable, the box  is at equilibrium - you can reasonably assume the box is at the same temperature as the surrounding atmosphere - if the box is an insulator, then you will have to know what the surrounding atmosphere is doing - graphed over time, the box will gradually reach thermal equilibrium again - just takins a while for a box with low thermal conductivity.  If temperature of the surrounding atmosphere is not available, if it is isolated from the universe - i.e. a box within a box, then pressure is a means of determining whether the interior of the box is in equilibrium.  once you can determine the box is in equilibrium, you can conclude the interior of the box is the same as the surrounding atmosphere - (the only conclusion without an actual measurement of temperature somewhere...)

Answer 2

assuming that there is a gas (no vacuum) then use the equation of state...PV=RT, solve for T. R=gas constant, 8.14J/K..., P=pressure V=volume.

Answer 3

You cannot determine the initial internal temperature if it is different from the ambient. However, if the box is not exposed to radiant heat and the ambient temperature is consistent, that temperature inside the box would sooner or later become the same temperature as that ambient temperature regardless of the construction of the box.

Use of the perfect gas equation  (as noted in an earlier response) could work only if you knew the mass of the non-condensed gas within the box and you were also allowed to use a pressure gage (but not a thermometer)..

Answer 4

Hi there,

As I understand, given a certain amount of time, the temp inside the box will be eventually equal to the ambient temp. If you look at the equation for the thermal conductivity, the diff in Temp will reach to zero when the time goes to infinite.

Since the problem doesnt mention any thing about time factor, it's necessary to assume that the box is sit there for a while.

Good luck! ^_^

Answer 5

THIS PROBLEM IS SOLVED WITH THE LAWS OF HEAT TRANSFER.WE MUST KNOW THE THICK OF WALL OF BOX , COEFFICIENT OF HEAT TRANSFER OF THE BOX ETC.

Answer 6

1. System dynamics approach. Determine the time constant for the heating/cooling of the box. After 5 time constants, within well under 1% of ambient from original temp. Go 10 time constants if you need it really, really, close.

2. Indirect thermometer approach. Put another box around the first. Wait 1 time period, measure increase in pressure of box. You can use PV=mRT to determine heat coming out, then back into internal temp.