[SOLVED] Phys 362 Statistical and Thermal Physics: Homework 8

A monoatomic ideal gas undergoes the process indicated on the P V diagram. The curved line is an
isothermal compression. The initial process at volume Vi reduces the pressure to one quarter of Pi.
Pi
Vi
P
Va) Determine the change in entropy, in terms of Pi
and Vi, along the constant volume process.b) Determine the change in entropy, in terms of Pi
and Vi, along the constant pressure process.c) Starting with the first law of thermodynamics and using the fundamental thermodynamic
identity show that along an isothermal process
dS = N k
V dV.
determine a general expression for the change
in entropy for an isothermal process.d) Determine the change in entropy, in terms of Pi and Vi, along the isothermal compression.
e) Determine the change in entropy for gas for the entire process.f) Does the gas do work for the entire process? Is heat supplied to the gas for the entire
process? Can this process occur so that the entropy of the system plus surroundings
does not increase?A block of zinc with mass 0.750 kg is initially at temperature 120 C. The zinc is immersed in
water with mass 1.25 kg and which is initially at temperature 20. The specific heat capacity
of water is 4.186 103 J/kg K and of zinc, 387 J/kg K.a) Determine the change in entropy of the zinc as it reaches equilibrium with the water.b) Determine the change in entropy of the water as it reaches equilibrium with the zinc.c) Determine the net change in entropy of the zinc and water.3 Gould and Tobochnik, Statistical and Thermal Physics, 2.62, page 106.Consider a system with heat capacity C that interacts with a heat bath. Suppose that the
system is initially at temperature Tsys and that the bath is a temperature TB. The two are
then placed in contact and during the process that follows the system remains at constant
volume.a) Show that the change in entropy of the system plus bath is
S = C
!
ln TB
Tsys #
+
Tsys
TB
1
$
and note that this involves a function of the form
f(x) = ln x +
1
x 1.b) Determine when f(x) attains a minimum and what this minimum is. Use this to describe
the condition under which S = 0.c) Use results from the previous part to describe whether the change in entropy is always
positive when the bath is initially at a lower temperature than the system.d) Use results from the previous part to describe whether the change in entropy is always
positive when the bath is initially at a higher temperature than the system.