What is the temperature in the empty box if there is one Joules inside?

Question

CUNY

Answer 1

The answer to your question would depend on (1) whether "empty" means a "perfect vacuum" or filled with air? (2) how is this 1 joule of energy initially distributed inside this box? (3) how large is this box? (4) how much time is allowed to elapse before the termperature is determined? (5) can energy leak out or into the box? (6) is the box under the influence of a gravitational field?

The temperature of an object is proportional to the average kinetic energy of the molecules in it. In a pure vacuum, there are no molecules. There is nothing to measure the kinetic energy of, and temperature is undefined. If a thermometer were placed in a vacuum, the reading would be a measurement of the internal temperature of the thermometer, not of the vacuum which surrounds it. So having 1 joule of energy inside a box containing pure vacuum would have NO temperature. And if it contained air, then we would need to know the initial temperature, pressure of the air inside the box and also the volume of the box. Then we can approximate the air as an ideal gas and use the following equation to compute the temperature:

PV=nRT

where T is the temperature, n is the number of moles of gas and R is the gas constant. Since we know the initial temperture and pressure, and the volume of the box. Then

P(i)V(i)/T(i) = P(f)V(f)/T(f)

T(f) = T(i) [P(f)/P(i)]

Since pressure is dfined as P = F/A (force per unit area) and

E = Fd (force times distance), then

P = E/Ad, where Ad = V volume of the box (here we are assuming that the 1 joule of energy is uniformly distributed inside the box and the volume of the box does not change)

Hence, T(f) = T(i) [E/P(i)V(i)]

Answer 2

I will help you out here. The units of a Joule is kg * m^2/s^2. If you can figure out how to calculate temperature in a box using the units kg * m^2/s^2 without any other units to work with then I think you can probably win a Nobel prize. If not, stop posting such an stupid question.

Answer 3

I can't give you the answer, because you give me very short information to calculate ( Q=mc(t2 - t1) )