Entropy involving ideal gases

Problem:

Calculate the entropy change of an ideal gas that undergoes a reversible isothermal expansion from volume V1 to V2.

Solution:

Problem:

Calculate the entropy change of 1 mole of an ideal gas that undergoes an isothermal transformation from an initial state of pressure 1.5 atm and a volume of 500 cm3 to a final state of pressure 0.90 atm.

Solution:

Problem:

One mole of an ideal gas is compressed at 60 oC isothermally from 5 atm to 20 atm.
(a)  Find the work done.
(b)  Find the entropy change for the gas and interpret its algebraic sign
Gas constant : 8.314 J/(mol K)

Solution:

Problem:

The figure below shows a maximally efficient Carnot cycle in the pressure-volume plane for a heat engine operating between two heat reservoirs to perform work.
(a)  For each label 1 through 4 identify the process, say whether work is done by the working fluid or on it and whether heat is added to the working fluid or extracted from it.
(b)  Make a diagram showing the same cycle in the temperature-entropy plane.  Label the parts of your diagram that correspond to the parts labeled in the P-V diagram and put arrows on each segment indicating the direction it is traversed.

image

Solution:

Problem:

A cylinder is partitioned by a membrane into a volume V1 initially filled with a classical ideal gas of N particles with no internal degrees of freedom at temperature T, and a volume V2 initially enclosing a perfect vacuum.
(a)  The cylinder is in contact with a heat reservoir at temperature T.  The membrane is moved slowly without friction, allowing the gas to fill the entire cylinder.  Compute the work done by the gas, the heat transferred between the gas and the heat bath, and the change in the entropy of the gas.  Is this a reversible process?
(b)  The cylinder is returned to its initial state and insulated from the heat bath.  The membrane is allowed to break, releasing the gas to fill the entire volume.  Assume that the expansion occurs essentially instantaneously, and a  new equilibrium is reached.  Compute the work done by the gas and the change in the entropy.  Is this a reversible process?

Solution:

Problem:

Consider a system of one mole of an ideal gas A and three moles of an ideal gas B at the same pressure P and temperature T, in volumes of VA and VB respectively.  The two gases are separated by a partition so they are each sequestered in their respective volumes.  If the partition is removed, calculate the change in entropy of the system.

Solution: