A 2.50 mole sample of an ideal gas, for which C v , m = 3 R / 2 , is subjected to two successive changes in state: (1) From 25 .0 ° C and 125 × 1 0 3 Pa , the gas is expanded isothermally against a constant pressure of 15 .2 × 1 0 3 Pa to twice the initial volume. (2) At the end of the previous process, the gas is cooled at constant volume from 25 .0 ° C to − 29 .0 ° C . Calculate q, w, Δ U , and Δ H for each of the stages. Also calculate q, w, Δ U , and Δ H for the complete process.
A 2.50 mole sample of an ideal gas, for which C v , m = 3 R / 2 , is subjected to two successive changes in state: (1) From 25 .0 ° C and 125 × 1 0 3 Pa , the gas is expanded isothermally against a constant pressure of 15 .2 × 1 0 3 Pa to twice the initial volume. (2) At the end of the previous process, the gas is cooled at constant volume from 25 .0 ° C to − 29 .0 ° C . Calculate q, w, Δ U , and Δ H for each of the stages. Also calculate q, w, Δ U , and Δ H for the complete process.
Solution Summary: The author defines a reversible process as the process which can be reversed to its original state. In an adiabatic process the heat change is zero therefore the work done will be equal to the change in the internal energy
A 2.50 mole sample of an ideal gas, for which
C
v
,
m
=
3
R
/
2
, is subjected to two successive changes in state: (1) From
25
.0
°
C
and
125
×
1
0
3
Pa
, the gas is expanded isothermally against a constant pressure of
15
.2
×
1
0
3
Pa
to twice the initial volume. (2) At the end of the previous process, the gas is cooled at constant volume from
25
.0
°
C
to
−
29
.0
°
C
. Calculate q, w,
Δ
U
, and
Δ
H
for each of the stages. Also calculate q, w,
Δ
U
, and
Δ
H
for the complete process.
1.1 mole of O₂ (g) and 2.2 moles of N₂ (g) are spontaneously mixed in a cylinder (volume = 30.0 L)
with a movable piston. Assume both gases are ideal.
(a)
Explain why the mixing of O₂ and N₂ gases is spontaneous in term of chemical
potential.
(b)
Calculate the final pressure (in N m2) of mixture when
(i) the mixing occurs isothermally at 298 K;
(ii) the initial temperatures of O₂ (g) and N₂ (g) are 306 K and 367 K, respectively, and after
mixing, the temperature is equilibrated. State any assumption(s) in your calculations.
(c)
) Now, the mixture in (b)(ii) is expanded isothermally and the external pressure is
suddenly decreased to a final pressure of 890 Torr, determine whether the process is reversible or
not.
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The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY