**P. 4511.** A sample of monatomic ideal gas is taken through the process shown in the *V*-*T* diagram of the *figure.* At state *A* the pressure of the gas is *p*_{0}, its volume is *V*_{0} and its temperature is *T*_{0}=200 K.

*a*) Draw the graph of the process on the *p*-*V* diagram.

*b*) Find that state *E* of the process on the *p*-*V* diagram for which it is true that the works done by the gas during the processes *A**E* and *E**D* are equal.

*c*) What is the temperature of the gas at state *E*?

*d*) By what factor the absorbed heat in process *A**E* is greater than that of in process *E**D*?

(4 points)

**P. 4513.** Two small insulating discs of mass *m* are placed to the horizontal tabletop, such that initially the distance between their centres is *x*_{0}=5 cm. A small metal sphere of charge *Q*=8^{.}10^{-8} C is fixed at the top of each disc.

One of the discs if fixed to the tabletop and the other is released, and it slides. The coefficient of friction between the disc and the tabletop is =_{0}=0.3. Neglect the electrostatic interaction between the charges and the tabletop.

*a*) What will the distance *x*_{1} be between the centres of the two discs at the moment when the speed of the sliding disc is maximal?

*b*) What will the distance *x*_{m} between the two discs be after the sliding discs stops?

*c*) What is the relationship between *x*_{0}, *x*_{1} and *x*_{m}?

(5 points)

**P. 4514.** The readings on the voltmeter and the ammeter connected to the circuit shown in the *figure* are 10 V and 200 mA, respectively when the switch is open. If the switch is closed the reading on the ammeter increases by 0.1 A, and the voltage across resistor *R*_{2} increases by 10 V.

*a*) What are the resistance values of the resistors?

*b*) What is the voltage of the voltage supply? *c*) What is the reading on the voltmeter when the switch is closed?

(4 points)

**P. 4515.** The opposite sides of the vertical conducting frame shown in the *figure* are parallel, and the top part is connected through a resistor of resistance *R*=2 ohm. The frame is in uniform magnetic field of *B* which is perpendicular to the plane of the frame. *B*=0.8 T. The distance between the parallel, vertical sides of the frame is =20 cm, and the mass of the piece of conductor of negligible resistance, which can slide along the vertical wires without friction is *m*=200 g. The piece of conductor is released with zero initial speed.

*a*) Graph the net force exerted on the piece of conductor as a function of the speed of the conductor.

*b*) Estimate how much time elapses while the speed of the conductor changes from 4 m/s to 4.2 m/s. How much distance does it cover during this?

(5 points)