Question

Ten liters of a monoatomic ideal gas at 25^{o} 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 gas after the reversible adiabatic expansion, verify that the change in U for the process is independent of the path taken between the initial and final states by considering the process to be carried out as:

i. An isothermal process followed by a constant-volume process

ii. A constant-volume process followed by an isothermal process

iii. An isothermal process followed by a constant-pressure process

iv. A constant-volume process followed by a constant-pressure process

v. A constant-pressure process followed by a constant-volume process

Answer #1

1) for isothermal and reversible process:

work done = = 1*8.14*298*ln(10) = 5.6kJ

U is proportional to change in temperature, so delta(U)= 0 as T is constant.

U=Q-W, so Q= 5.6kJ

delta(H) is also zero as delta (T) is zero

2) Adiabatic reversible process:

for an adiabatic process, no heat is added or removed from the system, so Q=0

we have
where
=5/3 for a monoatomic gas. putting the values we get,
V_{2}=40 litres

work done =
where K =PV^{gamma} = constant

putting values W = -90 J

Also W=delta(U) for adiabatic process

in the figure the five cases for the adiabatic process have addressed where the initial anf final points are fixed. the adiabatic process has been shown in dotted lines and the solid lines depict the processes named (i)-(v)

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.

) 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.

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...

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

One mole of an ideal gas at 300 K is expanded adiabatically and
reversibly from 20 atm to 1 atm. What is the final temperature of
the gas, assuming Cv= 3/2R.
Question 1 options: a) 400 K b) 250 K c)156 K d)90.5 K

A 2.5 mol sample of ideal gas initially at 1 atm and 25 °C is
expanded isothermally (ΔT = 0) and reversibly to twice its original
volume.
What is the change in internal energy?

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.

Four kilomoles of a monoatomic idel gas are at a temperature of
300 K. The gas expands reversibly and isothermally to twice its
original volume.
1) Sketch the process in the P-V plane.
2) Compute the work done by the gas.
3) Compute the heat supplied to maintain constant temperature.
Note U=U(T).

1 mole of ideal gas at 270C is expanded isothermally from an
initial pressure of 3 atm to afinal pressure of 1 atm in two ways:
(a) reversibly and (b) against a constant external pressure of 1
atm. Calculate q, w, ΔU, ΔH and ΔS for each path.

Use these steps to answer the questions below:
Step 1: A sample of monoatomic ideal gas, initially at pressure
P1 and volume V1, expands isothermally and
reversibly to a final pressure P2 and volume
V2
Step 2: The ideal gas is compressed isothermally back to its
initial conditions using constant pressure.
Give the equation needed to solve for the following
Wsys (Step 1)
=
qsys (Step 2)
=

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