(a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m * 12.00 m * 4.00 m if the air is treated as an ideal gas at 1.00 atm?

Video transcript

welcome back everybody. We are looking at air inside of a metallic tank and we are told that the dimensions of the tank are 10 m by six m by four m. Which if we multiply all that together gives us our volume of 240 m cubed. Now we are told that the air inside of the tank behaves like an ideal gas. We can say that the pressure is at standard conditions of 1 M. Or 1.13 times 10 to the fifth pascal's. And we are tasked with finding what the translational kinetic energy is inside of tank. Now the formula for this is three halves times N. R. T. But since we are dealing with a gas that behaves like an ideal gas, we can use the ideal gas law that says N. R. T. Is equal to pressure times volume, which I'm going to sub in right here. So our translational kinetic energy is really three halves times our pressure times volume. Let's go ahead and plug in our terms here that our translation kinetic energy is equal to three halves times 1.13 times 10 to the fifth time's a volume of 240 m cubed. Giving us a final answer of 3.65 times to the seventh jewels which corresponds to our answer choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one