16 PROBLEMSThe gas now expands adiabatically to volume What is the final
temperature (derive this resultfrom first principles)?
Estimate for K for air.b)c)4.26 Isochoric Cooling and Isobaric Expansion
(Moscow Phys-Tech)An ideal gas of total mass and molecular weight is isochorically (at con-
stant volume) cooled to a pressure times smaller than the initial pressure
The gas is then expanded at constant pressure so that in the final state
the temperature coincides with the initialtemperature Calculate
the work done by the gas.4.27 Venting (Moscow Phys-Tech)
A thermally insulatedchamber is pumped down to a very low pressure.
At some point, the chamber is vented so that it is filled with air up to
atmospheric pressure, whereupon the valve is closed. The temperature of
the air surrounding the chamber is What is the temperature
T of the gas in the chamber immediately after venting?4.28 Cylinder and Heat Bath (Stony Brook)
Consider a cylinder 1 m long with a thin, massless piston clamped in such
a way that it divides the cylinder into two equalparts. The cylinder is in
a largeheat bath at The leftside of thecylinder contains 1
mole of helium gas at 4 atm. The right contains helium gas at a pressure
of 1 atm. Let thepiston bereleased.
What is its final equilibrium position?
How much heat will be transmitted to the bath in the process of
equilibration? (Note thata)
b)4.29 Heat Extraction (MIT, Wisconsin-Madison)
a) A body of mass M has a temperature-independent specific heat C. If
the body is heated reversiblyfrom a temperature to a temperature
what is the change in its entropy?