The Second Law of Thermodynamics Flashcards
What does the second law state?
That work and heat cannot be interchanged without some flow of energy from or to the surroundings.
What is the Kelvin-Planck statement?
It is impossible to build a heat engine which converts thermal energy into work with 100% efficiency.
What is the Clausius statement?
Heat will not flow spontaneously from a cold body to a hot one.
What is meant by a cyclic process?
Process in which the substance ends in the same state as it started.
Explain the general principle of heat engines.
QH from hot reservoir goes to engine which exhausts QC to cold reservoir and Work.
What is the equation for efficiency of a heat engine.
Efficiency = W/QH
What is the Carnot Cycle?
A hypothetical idealised heat engine constructed from reversible processes.
What are the 4 stages in the p-V diagram of the Carnot cycle?
- 1 to 2 - Gas expands isothermally absorbing heat QH at temperature TH from hot reservoir
- 2 to 3 - Gas expands adiabatically, cooling to TC
- 3 to 4 - Gas is compressed isothermally, expelling heat to QC to cold reservoir at TC
- 4 to 1 - Gas is compressed adiabatically, heating to TH (original state)
What is the work done, internal energy and heat for the isothermal expansion step of the Carnot Cycle?
- W = nRTH * ln(V2/V1)
- QH = W
- ΔU = 0
What is the work done, internal energy and heat for the adiabatic expansion step of the Carnot Cycle?
- W = nCv ΔT = -nCV(TC-TH)
- Q = 0
- ΔU = -W = nCv (TC - TH)
What is the work done, internal energy and heat for the isothermal compression step of the Carnot Cycle?
- W = nRTC * ln(V4/V3)
- Qc = W = nRTC * ln(V4/V3)
- ΔU = 0
What is the work done, internal energy and heat for the adiabatic compression step of the Carnot Cycle?
- W = -nCvΔT = -nCv(TH-TC)
- Q = 0
- = -W = nCv(TH-TC)
What is the work done, internal energy and heat for the entire Carnot Cycle?
- W = W12 + W23 + W34 + W41
- Q = nR(TH-TC)*ln(V2/V1)
- ΔU = 0
How do you calculate the efficiency of a Carnot engine?
- E = work done per cycle/heat input per cycle = W/QH
- W = QH - QC
- E = 1-(QC/QH) = 1- TC/TH
What is the Carnot Refrigerator?
Run the Carnot cycle in reverse. All completely opposite to Carnot cycle.
What is a heat pump?
Heating a hot source from a cold source by doing work.
State Carnot’s Theorem.
The Carnot Cycle is the most efficient of all possible engines operating between the same two temperatures.
How can you proove Carnot’s Theorem?
- Assume an irreversible engine that is more efficient than the Carnot Cycle, connect it to a Carnot engine in reverse
- Qcc-Qcn = Qhc-Qhn > 0 - this means there is a transfer of heat with no work - not possible
State the third law of thermodynamics.
It is impossible to reduce the temperature of a body to absolute zero in a finite number of steps.
What is entropy?
The state variable associated with the order in a system. It is a quantitative measure of disorder.
What is the equation for entropy S?
ΔS = integral between 1 and 2 of dQrev/T
What is the entropy change for a reversible cyclic process?
ΔS = 0
What are the units of entropy?
JK^-1
What is the entropy for a reverisible process of the system and the surroundings?
ΔSsys = integral of dQ/T = ΔSsurr
What is the total entropy of a system and its surroundings?
ΔStot = ΔSsys + ΔSsurr = 0
What is the entropy for an irreversible process?
ΔS >= integral between 1 and 2 of dQ/T
How do you work out the entropy change when an ideal gas expands from V to 2V, without any work or temperature change?
Consider a reversible process between the two states - isothermal expansion. W = nRT*ln(2)
Q = W
ΔS = nRln(2)
What is the equation of the entropy of a macroscopic state?
S = kB ln(omega), where omega is the number of microstates
