A 1.0 kg ball is at rest on the floor in a 2.0 m x 2.0 m x 2.0m room of air at S
ID: 1728730 • Letter: A
Question
A 1.0 kg ball is at rest on the floor in a 2.0 m x 2.0 m x 2.0m room of air at STP. Air is 80% nitrogen (N2) and 20%oxygen (O2) by volume. a) what is the thermal energy of the air in the room? b) what fraction of the thermal energy would have to beconveyed to the ball for it to be spontaneously launched to aheight of 1.0 m? c) by how much would the air temperature have to decrease tolaunch the ball? d) your answer to part c is so small as to be unnoticeable,yet this event never happens. why not? A 1.0 kg ball is at rest on the floor in a 2.0 m x 2.0 m x 2.0m room of air at STP. Air is 80% nitrogen (N2) and 20%oxygen (O2) by volume. a) what is the thermal energy of the air in the room? b) what fraction of the thermal energy would have to beconveyed to the ball for it to be spontaneously launched to aheight of 1.0 m? c) by how much would the air temperature have to decrease tolaunch the ball? d) your answer to part c is so small as to be unnoticeable,yet this event never happens. why not?Explanation / Answer
STP means a pressure of 1atm (101300 Pa) and Temperature of 273K. I will use E to represent Thermal energy and U to represent potential energy a) Thermal Energy in the room (since they are N2 and O2 gasses we will use formula for diatomic gasses) E = 5/2 nRT. We know R & T, just need n and that can be obtained by pV=nRT n=pV/RT n= 357mol. just plug in the numbers and you will get the answer b) To lift a mass of 1KG to a height of 1m we need to do work, potential energy gained by the ball is change in thermal energy (thermal energy lost). U=mgh =1x9.8x1= 9.8J to find the fraction of energy needed just divide the energy lost by total thermal energy the gas had prior to launching the ball. c) This is similar to part a, just that you need to work backwards. You know new thermal energy of gas, T=2E/5nR This gives you the new temperature of the room, to find the change you subtract it from initial temperature. d) The chances of this ever occurring are astronomically small, this is explained by entropy
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