**P. 4476.** Kate invited her friends to her birthday party. She wanted to endear herself to her friends by making them some ice-cream. She mixed the ice-cream powder with water at 4 o'clock in the afternoon, her friends were invited to come to 6 o'clock, and she was a bit worrying whether the ice-cream will be ready or not. In order not to worry so much, she measured how fast the initially 25 ^{o}C ice-cream mixture cools down in the freezer. She observed that after 10 minutes the temperature of the ice-cream was 21 ^{o}C. Was she able to serve the ice-cream to her friends in the party if the party lasted until 10 at night, and the ice-cream must cool down to at least -6 ^{o}C? (Suppose that the heat extraction of the freezer is uniform, and the thermal properties of the liquid ice-cream and the ice-cream are the same as those of the water and ice.)

(4 points)

**P. 4479.** An easily moveable, insulated piston, of cross section *A*=2 dm^{2} and of mass *m*=5 kg, confines some air in a vertical thermally insulated cylinder. The air is heated by a heating element of power 200 W.

*a*) What is the speed of the piston?

*b*) By what amount does the internal energy of the air change in 2 s?

(5 points)

**P. 4481.** A big piece of positively charged metal sheet is illuminated by light of wavelength . The surface charge density of the metal is , and the work function of the metal is *W*.

*a*) At what greatest distance from the metal can electrons be found?

*b*) At what speed do the electrons moving back to the sheet hit the sheet?

(*Data:* =2^{.}10^{-6} C/m^{2}, *W*=0.41 aJ, =400 nm.)

(4 points)

**P. 4483.** If it was possible to create a vacuum tube along the magnetic equator of the Earth, the protons and electrons in this tube would - theoretically - orbit along circular path, due to the magnetic field of the Earth.

*a*) Estimate the speed and the direction of their motion.

*b*) What would the energy of these particles be in eV?

*c*) Can particle beams having the above calculated energy be created nowadays?

*d*) How much would the light, which travels along the same ``circle'' due to appropriately placed mirrors, overtake the particles travelling in the tube in one circle?

(5 points)