# Ideal Gas Law and kinetic energy

1. Nov 13, 2008

### snoopygal327

1. The problem statement, all variables and given/known data
An empty room in a house near the Atlantic coast has a volume of 45m3. What is the kinetic energy of all of the gas molecules in the room on a 30C summer day?

2. Relevant equations
pv = nrt

3. The attempt at a solution
I realize that this is an ideal gas law problem, but I have no idea where to start. How can I solve for anything if I'm only given volume and temperature?

2. Nov 13, 2008

### LowlyPion

You are on the right track. Maybe start here?
http://en.wikipedia.org/wiki/Kinetic_theory#Temperature_and_kinetic_energy

3. Nov 13, 2008

### snoopygal327

Okay, so I use the equation PV = (2/3)K. I assumed that the pressure is the standard 1 atm. Plugging everything into the equation:

101300 Pa (45 m3) = (2/3)K
K = 6837750 J

But the computer is telling me that this is the wrong answer. Did I do something wrong?

4. Nov 13, 2008

### LowlyPion

I think perhaps you want to use the relationship that KE = 3/2*k*T
That gives you the KE per particle and you can figure the number of particles from the Volume at 30° C = 303° K.
The k here is Boltzmann's constant 1.38 *10-23 J/°K

Noting that the volume of air occupied by 1000 moles of air is given here:
http://en.wikipedia.org/wiki/Standard_conditions_for_temperature_and_pressure

With 41 (1000/24.466) moles of air per m3 *45 m3 ... then you should be able to figure the total KE for that many moles of air in a 45 m3 room.