Question

It is possible to go from a given initial equilibrium state of a
system to a given final equilibrium state by a number of different
paths, involving different intermediate states and different
amounts of heat and work. Since the internal energy of a system is
a state function, its change between any two states must be
independent of the path chosen. The heat and work flows are,
however, path-dependent quantities and can differ on different
paths between given initial and final states. This assertion is
established here by example. One mole of a gas at a temperature of
25oC and a pressure of 1 bar (the initial state) is to be heated
and compressed in a frictionless piston and cylinder to 300oC and
10 bar (the final state). Compute the **entropy
change** (?S) along each of the following paths.

Path A: Isothermal (constant temperature) compression to 10 bar,
and then isobaric (constant pressure) heating to 300 oC

Path B: Isobaric heating to 300 oC followed by isothermal
compression to 10 bar

Path C: A compression in which Cp = (PV)^gamma , where gamma = Cp/Cv , followed by an isobaric colloing or heating, if necessary, to 300oC

Cp = 38 J/(mol K)

Answer #1

An insulated cylinder is filled with nitrogen gas at 25ºC and
1.00 bar. The nitrogen is then compressed adiabatically with a
constant pressure of 5.00 bar until equilibrium is reached. i. What
is the final temperature of the nitrogen if it is treated as an
ideal gas with molar heat capacity CP = 7/2 R ?
ii. Calculate ΔH (in kJ mol-1 ) and ΔS (in J mol-1 K-1 ) for the
compression. (Hint: Because the enthalpy is a state...

) An ideal gas (Cp = 5 kcal/kmol, Cv = 3
kcal/kmol) is changed from 1 atm and 22.4 m3 to 10 atm
and 2.24 m3 by the following reversible process
(i) Isothermal
compression
(ii) Adiabatic
compression followed by cooling at constant volume
(iii) Cooling at
constant pressure followed by heating at constant volume
Calculate the heat, work requirement,
?U and ?H for each
process.

Ten liters of a monoatomic ideal gas at 25o C and 10
atm pressure are expanded to a final pressure of 1 atm. The molar
heat capacity of the gas at constant volume, Cv, is 3/2R and is
independent of temperature. Calculate the work done, the heat
absorbed, and the change in U and H for the gas if the process is
carried out
(1) isothermally and reversibly, and
(2) adiabatically and reversibly.
Having determined the final state of the...

Steam undergoes an isentropic compression in an insulated
piston–cylinder assembly from an initial state where T1 = 120°C, p1
= 1 bar to a final state where the pressure p2 = 20 bar. Determine
the final temperature, in °C, and the work, in kJ per kg of steam.
The final temperature equals 513.87°C.

3. 10.0 moles of ideal gas cloud has an initial pressure of 1.00
bar, initial volume of 100.0L and temperature of 25.0ºC. The cloud
expands adiabatically to a final volume of 1000.0L. Cp,m= 20.79 J /
mol K (Cp,m is molar heat capacity and constant pressure)
a. (10 pts) What is the final pressure of the gas cloud?
b. (10 pts) What is the final temperature of the gas cloud?
c. (10 pts) What is the change in entropy for...

A 5 kg mass of R134a refrigerant is compressed
polytropically from the state initial: p1 = 1 bar, T1 = 27 ° C
until the final state: p2 = 15 bar, T2 = 227 ° C. Specific heat
R134a medium at constant volume, Cv = 0.72 kJ / kg K.
Calculate:
a) exponent of polytropy;
b) final volume;
c) final volume using the virial state equation d) work done on the
gas for compression;
e) amount of heat given up...

2 moles of a monatomic perfect gas (initial state A and final
state C) undergo an isobaric expansion AB followed by an adiabatic
expansion BC.
TA= 18 C
PA= 2*10^5 Pa
VB= 0,048m^3
Calculate TB and the amount of heat Q exchanged in the
transformation from A to C.

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
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isothermal expansion occurs at the hot reservoir temperature of
Thot=600C from an initial volume of 3.50 L to a...

One mole of ideal gas initially at 300 K is expanded from an
initial pressure of 10 atm to a final pressure of 1 atm. Calculate
ΔU, q, w, ΔH, and the final temperature T2 for this expansion
carried out according to each of the following paths. The heat
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1. A reversible adiabatic expansion.

An air compressor, operated at steady state, compresses air from
1 bar 25oC to 10 bar. At the outlet of the compressor,
the air temperature is 80oC. The compressor transfers
heat to the surroundings at 300kJ for each kg of air passing
through the compressor. The average temperature at which the heat
is transferred is 50oC. Which of the following values is
closest to the specific entropy production of the compressor
process? For air, Cp=1.01 kJ/kgK and R=0.286kJ/kgK. Hints: Air...

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