Replacing V 2 /V 1 in Eq. (4.10) by P 1 /P 2 , We
have
Wmax = -2.303 nRT log
P 1
P 2(4.11)Problem 4.4 : 2 moles of an ideal gas are
expanded isothermally and reversibly from
20 L to 30 L at 300 K. Calculate the work
done (R= 8.314 J K-1 mol-1)
Solution : Wmax = -2.303 nRT log 10V 2
V 1
n = 2 mol, T = 300 K, V 1 = 20 L, V 2 = 30 L,
R = 8.314 J/K mol
Substitution of these quantities into the
equation gives
Wmax = -2.303 × 2 mol × 8.314 J/K mol^ ×
300K × log 10 30 L
20 L
= -2.303 × 2 × 8.314 J×300 × log 10 1.5
= -2.303 × 2 × 8.314 J×300 × 0.1761
= -2023 J = -2.023 kJProblem 4.5 : 22 g of CO 2 are compressed
isothermally and reversibly at 298 K from
initial pressure of 100 kPa when the work
obtained is 1.2 kJ. Find the final pressure.
Solution :
W = -2.303 nRT log 10P 1
P 2
n = 44 g mol22 g -1 =0.5 mol, T = 298 K,P 1 = 100 kPa, W = 1.2 kJ = 1200 JHence, 1200 J = -2.303 × 0.5 mol ×8.314 JK-1 mol-1 × 298K × log 10100 kPa
P 2or log 10 100 kPa
P 2=-1200
2.303 ×0.5 ×8.314 ×298
= -0.4206
100 kPa
P 2 = antilog (-0.4206) = 0.3797Therefore, P 2 =100 kPa
0.3797 = 263.4 kPaProblem 4.6 : 300 mmol of an ideal gas
occupies 13.7 dm^3 at 300 K. Calculate the
work done when the gas is expanded until
its volume has increased by 2.3 dm^3 (a)
isothermally against a constant external
pressure of 0.3 bar (b) isothermally and
reversibly (c) into vacuum.
Solution :
a. W = -Pex ∆V
Pext = 0.3 bar, ∆V = 2.3 dm^3
W = -0.3 bar × 2.3 dm^3
= -0.69 dm^3 bar
= -0.69 dm^3 bar ×100 J
dm^3 bar^
= - 69 J
b. Wmax = - 2.303 nRT log 10V 2
V 1
n = 300 mmol = 300 × 10-3 mol = 0.3 mol,
T = 300 K
Wmax = - 2.303 × 0.3 mol × 8.314 J K-1mol-1× 300K × log 1016
13.7
= -2.303 ×0.3 ×8.314 J ×300 ×0.0674
= - 116.1 J
c. W = - Pex ∆V
When gas is expanded to vaccum, Pext = 0
and W = 04.6 Internal energy (U) : Every substance is
associated with a definite amount of energy.
This energy stored in a substance is internal
energy denoted by U.
The internal energy of a system is made up
of kinetic and potential energies of individual
particles of the system.
∆U = U 2 - U 1
where U 1 and U 2 are internal energies of initial
and final states, respectively. U is a state
function and extensive property.