What is meant by the term the entropy of a system
Question three
(a) What is meant by the term the entropy of a system?
= The entropy of a system is referred to as the measure of randomness or disorder of a system, it also describes how much energy is not available to do work. The more disordered a system and the higher the entropy, the less of a system’s energy is available to do work.
(b) Show that the entropy change of a system at constant pressure is governed by the equation Cp In (T2/T1)
ANSWER
Pressure = (p)
CP = The heat capacity
CPdt = dqp then divide through with T
CPdt/T = dqp/T
But Dqp/T = ΔS
ΔS = dqp/t = CPdt/t
Integrating T1 → T2
ΔS = ∫T1T2 CPdt/T = CP∫T1T2 dt/T
ΔS = CPIn(T)T2/T1
ΔS = CP = (InT2-T1) = CPIn (T2/T1)
CP = In(T2/T1)
ΔS = CPIn(T2/T1)
(c) At 1 atmosphere, Toluene (methyl benzene) boils at 110oc and its latent heat of vaporization is 33470J/mol. Estimate the entropy change when Toluene is heated from 100oc to 130oc assuming that in this temperature range the heat capacities (Cp) of the liquid and the vapor are180JK-1mol-1 and 120JK-1mol-1 respectively.
ANSWER
100°c → 110°c CP = 180
110°c → 130°c CP = 120
Converting to kelvin
(100 + 273) = 373K T1
(110+273) = 383K T2
ΔS1 = CPIn(T2/T1)
= 180In(383/373)
= 4.76JK-1mol-1
ΔS2 = ΔQ/ΔT2
= 33470/383
= 87.39JK-1mol-1
ΔS3 = 120In(403/383) Note, Here, T2 = 130 + 273 = 403
= 6.11JK-1mol-1
ΔST = ΔS1+ΔS2 +ΔS3 = 4.76 + 87.39 + 6.11 = 98.26 JK-1mol-1
(d)A steam engine operates between 200K and 500K. What is the minimum amount of heat that must be withdrawn from the hot reservoir to obtain 1000 joules of work?
ANSWER
TC (Cold) = 200k
TH (Hot) = 500K
W = 1000J
Efficiency = TH – TC/TH =W/QH
= 500 – 200/500 = 1000/QH
QH = 0.6
Q = 1666.67J Which is the amount of heat required to be withdrawn from the reservoir.
