P114 Summer’05

Extra Credit #1

Due July 21, 2005

Team #____________

Member #1_____________________

Member #2_____________________

Member #3_____________________

Please staple team members’ pages together, with this being the cover page, fill in the top lines above. Each page should show the author’s name.

1.- Explain how do hot balloons work (rising and landing). Develop equations to calculate how much heat is needed to lift a hot balloon with mass M (excluding air), and volume V.

2.- The ideal Carnot engine shown below operates between a heat reservoir and a block of ice with mass M. An external energy source maintains the reservoir at a constant temperature At time the ice is at its melting point but it is insulated from everything except the engine, so it is free to change state and temperature. The engine is operated in such a way that it extracts heat from the reservoir at a constant rate P_h. (a) Find an expression for the time at which the ice is all melted, in terms of the quantities given and any other appropriate thermodynamic parameters. (b) Find an expression for the mechanical power output of the engine as a function of time for times

3.- Design one experiment to demonstrate the connection between the average kinetic energy of a liquid and its temperature, using two identical transparent cups, for example.