Physics Help

Question

A room of 1.5 litres contains gas with pressure 10^5 Pa.If the gas particle has average speed of 750 m/s,then gas mass that trapped in the room is...gram

A.0.8
B.0.7
C.0.6
D.0.5
E.0.4

Answer 1

This is a kinetic theory problem where pressure is related to how fast the particles are moving and how dense the gas is. The key idea is that P=(1/3)(rho)(v)^2. First convert the volume since it is in litres, so 1.5 litres is 1.5x10^(-3) cubic meters.

Now solve for density using the formula, so rho=3P/(v^2). That is 3x10^5/750^2. 750^2 is 562500 so you get about 0.533 kilograms per cubic meter.

Now multiply by the volume to get mass. That gives 0.533x[1.5x10^(-3)] which is about 0.0008 kilograms. Converting to grams gives 0.8 grams.

So the answer is 0.8 and the main thing here is recognizing they want you to use the kinetic theory relation since they gave you the speed directly.