Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

2. Heat and Molecular Physics 59

the right part is empty. The piston is con-

nected to the right wall of the vessel

through a spring whose length in free state is

equal to the length of the vessel (Fig. 64).

Pig. 64

Determine the heat capacity of the sys-

tem, neglecting the heat capacities of the

vessel, piston, and spring.

2.14. Prove that the efficiency of a heat en-

gine based on a cycle consisting of two iso-

therms and two isochors is lower than the

efficiency of Carnot's heat engine operating

with the same heater and cooler.

2.15*. Let us suppose that a planet of mass

M and radius r is surrounded by an atmo-

sphere of constant density, consisting of

a gas of molar mass R.

Determine the temperature T of the at-

mosphere on the surface of the planet if the

height of the atmosphere is h (h <r).

2.16. It is known that the temperature in

the room is +20 °C when the outdoor tem-

perature is —20 °C, and +10 °C when the

outdoor temperature is —40 °C.

Determine the temperature T of the ra-

diator heating the room.