Estimation of Change in Temperature

When Matt Threw the Tennis Ball

from the Top of the Lecture Hall

This is an energy conversion process. There are two forms of energy that are being converted. 1) Blood sugar goes to waste heat and to kinetic energy of the ball (which then both go to internal energy of the air in the room). 2) Potential energy goes to internal energy of the air in the room. For simplicity, we assumed that all the energy went into the air in the room and not into the people, the chairs, the floor and ceiling, etc. We also assumed that we could consider all the air in the room as the system and that a single value of temperature described the entire room (in reality there were temperature variations in the room). Finally, we assume that the room was well-insulated and nothing else was changing as a result of the b all being thrown. (This was clearly not the case. When Matt was getting ready to throw the ball, the excitement in the room was so palpable, that I am sure people we burning extra calories/Joules.)

The point of the experiment was to show how you use specific heats.

Here is the data that you folks gave me (I take no responsibility for the accuracy of these estimates):

1) velocity of ball = 5m/s

2) mass of ball = 0.2 kg

3) Matt's self-proclaimed efficiency = 21%

4) change in height = 3.5m

5) g = 9.8m/s2

6) density of air in room = 1.225 kg/m3

7) cv = 716.5 J/kg-K

8) Volume of air in room = 340 m3

Kinetic energy of the ball = 1/2mv2 = 2.5 J

The total energy that Matt used from his blood sugar to make this happen was 2.5J/0.21 = 11.9 J

The change in potential energy of the ball was mgh= 6.9 J

The sum of these two is the amount the internal energy of the air in the room will rise (given all the caveats described above) based on the First Law of Thermodynamics. So the change in internal energy of the air in the room was 18.8 J. To calculate the temperature change I will use du=cv(dT), or dU=m(cv)dT. The mass of air in the room is 340(1.225)=416.5kg. Therefore the change in temperature was 18.8/416.5/716.5 = 6.3 E-05 K, which explains why I was sweating so much.