Question

Two ideal gas systems undergo reversible expansion starting from the same P and V. At the end of the expansion, the two systems have the same volume. The pressure in the system that has undergone adiabatic expansion is lower than that in the system that has undergone isothermal expansion. Explain this observation without using equations.

Answer #1

The work done in a system undergoing Adiabatic expansion generally comes through the lowering of Internal Energy of the system (U) and the temperature. In the system undergoing adiabatic expansion, all the work done must come through the lowering of ΔU, and therefore of the temperature. But, in case of isothermal expansion work done is carried out by the flow of heat across the boundary between the system and the surroundings.

That's the reason, pressure in the system is lowered in an adiabatic expansion rather than an isothermal expansion.

Suppose 4.00 mol of an ideal gas undergoes a reversible
isothermal expansion from volume V1 to volume V2 = 8V1 at
temperature T = 300 K. Find (a) the work done by the gas and (b)
the entropy change of the gas. (c) If the expansion is reversible
and adiabatic instead of isothermal, what is the entropy change of
the gas?

An ideal gas at 300 K has a volume of 15 L at a pressure of 15
atm. Calculate the:
(1)the ﬁnal volume of the system,
(2) the work done by the system,
(3) the heat entering thesystem,
(4) the change in internal energy when the gas undergoes
a.- A reversible isothermal expansion to a pressure of 10
atm
b.- A reversible adiabatic expansion to a pressure of 10
atm.

Calculate the total change of entropy for an ideal monatomic gas
expanding from a volume V into a volume 2V via: i) Free expansion
ii) Quasi-static isothermal expansion iii) Quasi-static adiabatic
expansion; iv) Do the results of (iii) surprise you? Comment on
what these results mean in terms of reversible and irreversible
processes.

7. 1.55 moles of Argon gas undergo an isothermal reversible
expansion from an initial volume of 5.00 L to 105. L at 300 K.
Calculate the work done during this process using: (a) the ideal
gas equation, and (b) the van der Waals equation of state. Van der
Waals parameters for Ar are available in the back of the book.
Compare the two results, what percentage of the work done by the
van der Waals gas arises due to having...

A Joule expansion refers to the expansion of a gas from volume
V1 to volume V2 against no
applied pressure, and is sometimes also called a free expansion.
There is no work done, because the P of -PdV is
zero. By insulating the system, this process can be done
adiabatically, so there is no change in heat. For an ideal gas, the
adiabatic process is also isothermal, so there is no change in
thermodynamic energy, ∆U = 0 (which is...

Thermodynamics Question
A Joule expansion refers to the expansion of a gas from volume
V1 to volume V2against no
applied pressure, and is sometimes also called a free expansion.
There is no work done, because the P of -PdV is
zero. By insulating the system, this process can be done
adiabatically, so there is no change in heat. For an ideal gas, the
adiabatic process is also isothermal, so there is no change in
thermodynamic energy, ∆U = 0 (which...

Calculate the change in entropy for one mole of ideal gas which
expands from an initial volume of 2 L and initial temperature of
500 K to a final volume of 6 L under the following conditions.
P(initial) refers to the pressure when T(initial)= 500K,
V(initial)= 2 L.
a) Irreversible expansion against a constant pressure of
Pinitial/2
b) Irreversible expansion against a vacuum...a 'free
expansion'.
c) Adiabatic irreversible expansion against a constant pressure
of Pfinal
d) Adiabatic reversible expansion

Two containers, A and B, contain equal amount of the same ideal
gas occupying the same volume, and at the same temperature
initially. Container A is fitted with a moveable
piston, while volume of container B is fixed. Then
equal amount of heat is added to both systems. When heat is added
to container A, it expands. How do the final temperatures of the
two systems compare and why?
a) System A has a final higher temperature than B due...

6. Consider an ideal gas that undergoes isothermal (constant
temperature) expansion from state “1” to state “2” along two
different paths: a) reversibly and b) irreversibly. For these two
paths, compare the relative magnitude (i.e. greater/same/lower) of
the expansion work that ideal gas does to the surroundings. Make
sure to justify your answer (suggestion to use a P-V diagram).

a) Calculate delta S(system) for the reversible heating of 1 mol
of ethane from 298K to 1500 K at constant pressure. Use Cp = 5.351
+ 177.669x10-3 T – 687.01x10-7 T ^2 + 8.514x10-9 T ^3 (J/mol K).
Consider the reversible Carnot cycle discussed in class with 1 mol
of an ideal gas with Cv=3/2R as the working substance. The initial
isothermal expansion occurs at the hot reservoir temperature of
Thot=600C from an initial volume of 3.50 L to a...

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