**P. 3955.** There are two samples of gas in a thermally insulated cylinder. One of them is Argon at a temperature of 300 K, and the other is Nitrogen at a temperature of 400 K. There is a thermally insulated wall between them. The two gases have the same pressure and the same volume. Then the wall between the gases is taken away, and the two gases mix.

*a*) Does the energy of the system change?

*b*) What will be the common temperature?

*c*) How does the pressure change?

*d*) Does the entropy of the system change?

(5 points)

**P. 3960.** A vertical cylinder of radius *R* is fixed on a horizontal, ideally smooth tabletop. There is a string attached to the bottom of the cylinder, while to the other end of the string a small disc, whose mass is *m*, is fixed. The small disc is given a velocity *v*_{0} which is perpendicular to the tightened string. The disc slides on the tabletop while the string is wound round the cylinder. *a*) What is the velocity of the small disc when it hits the wall of the cylinder? (Give both the direction and the magnitude.) *b*) What is the tension at this moment? (*Data:* *R*=1 m, *l*_{0}=2 m, *r*=2 cm, *m*=5 g.)

(5 points)