# Calculate the power temperature

1. Jan 19, 2010

### JQ10

Edit: Topic title should read power and temperature

1. The problem statement, all variables and given/known data

Humans convert most of a 2000 kcal typical daily diet into heat. Calculate the power. What is the increase of temperature in a room with a volume of 15000 m^3 filled with 250 people over a 60 minute period?

Note: Power is defined as energy/time.
1kcal = 4.186kJ.
density of air = 1.29kg/m^3
molar mass of air = 29g
Treat air as a diatomic gas

2. Relevant equations

C = change in internal energy/ number of moles * change in temperature = f/2*R

3. The attempt at a solution

60 * 60 = 3600

2000 * 4.186 = 8372kJ/3600s = 2.3kJ/s = 2.3W

Specific Heat Capacity = 5/2 * R = 5/2 * 8.31 = 20.8 kJ/moleK

I'm really struggling with where to take it from there. I'd guess you would either use change in internal energy/ number of moles * change in temperature or use average kinetic energy = 5/2kT = 1/2mv^2rms but I'm not sure how to calculate the relevant data for either plus that doesn't use all the information given.

Last edited: Jan 19, 2010
2. Jan 19, 2010

### Yitzach

I have not played with attempting the find the specific heat of air before so I'll let someone else help you there. I can tell you that the power involved is not 2.3 W because there are not 3600 seconds in a day. Note that the problem said "daily." And a watt is not equal to kJ/s but J/s. Due to those two errors, your power is small by an order of magnitude.

3. Jan 19, 2010

### JQ10

Thank you for the help.