Ideal Gas Law and kinetic energy

[snoopygal327]

Homework Statement

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?

Homework Equations

pv = nrt

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?

 

[LowlyPion]

Homework Statement

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?

Homework Equations

pv = nrt

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?

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

 

[snoopygal327]

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

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?

 

[LowlyPion]

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?

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:

V/n = 8.3145 × 298.15 / 101.325 = 24.466 m3/kmol at 25 °C and 101.325 kPa

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.