Question

Ideal gas ethylene undergoes a reversible adiabatic compression by which its temperature increases from T1 = 300 K to T2 = 450 K. The molar entropy in the initial state is given as s1 = 100 J K–1 mol–1, and here, for ethylene, cp = ?T + c0 with ? = 0.1 J K–2 mol–1 and c0 = 13.1 J K–1 mol–1. Determine the change of the molar entropy s2 – s1 and the change of the chemical potential ?2 – ?1 for the fluid during this process.

Answer #1

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?

N moles of this gas undergoes the following cyclical process
composed of four reversible steps:
i. Isovolumetric cooling from state 1 (T1 and P1) to State 2 (T2
and P2);
ii. Isothermal expansion from state 2 (T2 and P2) to state 3 (T2
and P3);
iii. Isovolumetric heating from state 3 (T2 and P3) back to
state 4 (T4 and P4); and
iv. Adiabatic compression from state 4 (T4 and P4) to state 1
(T1 and P1).
We know that...

Consider the adiabatic, reversible expansion of a closed 1 mole
sample of monatomic ideal gas from P1 = 100 bar, V1 = 1dm3, and T1
= 1200K to V2 = 1.5 dm3.
What is the final temperature of the gas? What are the values of
ΔE, ΔS and w for the process described in the previous question? ΔE
= kJ ΔS = J/K w = kJ

Assume that one mole of a monatomic (CV,m = 2.5R) ideal gas
undergoes a reversible isobaric expansion at 1 bar and the volume
increases from 0.5 L to 1 L. (a) Find the heat per mole, the work
per mole done, and the change in the molar internal energy, ΔUm,
the molar enthalpy, ΔHm, for this process. b) What are the entropy
changes ΔSm of the system and of the surroundings? Is this process
spontaneous? Justify your answer.

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...

Determine the final specific volume (m3/kg) for a gas undergoing
a process from state 1 (T1 = 324 K, v1 = 0.2353 m3/kg) to a
temperature of T2 = 883 K if s2 - s1 = 0.961 kJ/kg-K. Assume
constant specific heats as given below (DO NOT USE the ideal gas
tables).
Cp = 1.135 kJ/kg-K
Cv = 0.759 kJ/kg-K
Note: Give your answer to four decimal places.
Correct Answer:
[Correct] 0.4006 ± 1%
Please show your methodology.

In class we discussed a reversible, isothermal compression of an
ideal gas. The initial point (1) is an ideal gas in equilibrium at
pressure 1 (P1), volume 1 (V1) and temperature (T), and the final
point (2) is an ideal gas in equilibrium at pressure 2 (P2), volume
2 (V2) and temperature (T), where V2
d) For each differential step, the change in entropy is given by
dS=qrev/T =!!!"#! . Since T is constant , this express ion can be...

2.)1.0 mol sample of an ideal monatomic gas originally at a
pressure of 1 atm undergoes a 3-step process as follows:
(i) It expands
adiabatically from T1 = 588 K to T2 = 389 K
(ii) It is compressed at
constant pressure until its temperature reaches T3 K
(iii) It then returns to its
original pressure and temperature by a constant volume process.
A). Plot these processes on a PV diagram
B). Determine the temperature T3
C)....

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...

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