Question

a. One mole of an ideal monoatomic gas (closed system, Cv,m) initially at 1 atm and 273.15 K experiences a reversible process in which the volume is doubled. the nature of the process is unspecified, but the following quantities are known, deltaH=2000.0J and q=1600.0J. Calculate the initial volume, the final temperature, the final pressure, deltaU, and w for the process.

b. Suppose the above gas was taken from the same initial state to the same final state as in the first part, but by a two step process consisting of first a reversible, isobaric step and then a reversible, isothermal step. Draw a diagram of P vs T indicting the overall change of state and the two step pathway. Calculate the overall deltaH, deltaU, deltaw, and q for the two step process.

Answer #1

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...

3 moles of a monoatomic ideal gas with Cv=(32)RT occupies a
volume of 3.2L at a pressure of 1.9atm at point A. The gas is
carried through a cycle consisting of three processes:
1. The gas is heated at constant pressure until its volume is 4.4L
at point B.
2. The gas is cooled at constant volume until the pressure
decreases to 1.2atm (C).
3. The gas undergoes an isothermal compression back to point
A.
Find W for the isochoric...

A 2.0 mol sample of ideal gas with molar specific heat
Cv = (5/2)R is initially at 300 K and 100 kPa pressure. Determine
the final temperature and the work done on the gas when 1.6 kJ of
heat is added to the gas during each of these separate processes
(all starting at same initial temperature and pressure: (a)
isothermal (constant temperature) process, (b) isometric (constant
volume) process, and (c) isobaric (constant pressure) process.
Hint: You’ll need the 1st Law...

5 mole of an ideal gas for which Cv,m=3/2R, initially at 20 oC
and 1 atm undergoes a two-stage transformation.
For each of the stages described in the following list,
Calculate the final pressure as well as q, w, ∆U, ∆H and ∆S.
a) The gas is expanded isothermally and reversibly until the
volume triple.
b) then, the temperature is raised to T=2000 oC at the constant
volume. Note: R= 8.314 j/mol.K or 0.082 lt.atm/mol.K, 1lt.atm=
101.325 joule

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.

2.25 moles of an ideal gas with Cv,m = 5R/2 are transformed
irreversibly from an initial
state T = 680 K and P = 1.15 bar to a final state T= 298 and P=
4.75 bar.
a) Calculate ΔU, ΔH, and ΔS for this process.
b) Calculate ΔU, ΔH, and ΔS for this process was reversible.

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
capacity of an ideal gas is cV=3R/2.
1. A reversible adiabatic expansion.

A cylinder contains an ideal gas at the temperature of 300 K and
is closed by a movable piston. The gas, which is initially at a
pressure of 3 atm occupying a volume of 30 L, expands isothermally
to a volume of 80 L. The gas is then compressed isobarically,
returning to its initial volume of 30 L. Calculate the work done by
gas: a) in isothermal expansion; b) in isobaric compression, c) in
the whole process; and d) Calculate...

A 1.65 mol of an ideal gas (Cv=3R/2) at T=14.5 oC and P=0.2 bar
undergoes the following two step process: first an isothermal
expansion against a constant pressure of 0.1 bar until the volume
is doubled; followed by a cooling to -35.6 oC at constant volume.
Calculate the following thermodynamic quantities for the total
process:
1) Work (w) for step 1.
2) Heat (Q) for step 1.
3) Change in internal energy (U) for step 1.
4) Change in enthalpy...

2.15 mol of an ideal gas with CV,m=3R/2
undergoes the transformations described in the following list from
an initial state described by T=350.K and
P=5.00bar.
1) The gas undergoes a reversible adiabatic expansion until the
final pressure is one-fourth its initial value.
2) The gas undergoes an adiabatic expansion against a constant
external pressure of 1.25 bar until the final pressure is
one-fourth its initial value.
3)The gas undergoes an expansion against a constant external
pressure of zero bar until...

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