Thermodynamics 2 Flashcards
Efficiency of a Heat Engine
ε = W/Qh = 1 - Qc/Qh
Coefficient of Performance of a Refrigerator
COP = Qc/W
Coefficient of Performance of a Heat Pump
COPhp = Qh/W
Heat Engine Equation
Qh = W + Qc
Second Law of Thermodynamics
The Kelvin Statement
No system can absorb heat from a single reservoir and convert it entirely into work without additional net changes in the system or its surroundings.
Second Law of Thermodynamics
The Heat-Engine Statement
It is impossible for a heat engine working in a cycle to produce only the effect of absorbing heat from a single reservoir and performing an equivalent amount of work.
Second Law of Thermodynamics
The Claussias Statement
A process whose only net result is to absorb heat from a cold reservoir and release the same amount of heat to a hot reservoir is impossible.
Second Law of Thermodynamics
The Refrigerator Statement
It is impossible for a refrigerator working in a cycle to produce only the effect of absorbing heat from a cold object and releasing the same amount of heat to a hot object.
Second Law of Thermodynamics
The Entropy Statement
The entropy of the universe (system plus surroundings) can never decrease.
Conditions for a Reversible Process
1) No mechanical energy is transformed into internal thermal energy by friction, viscous forces, or other dissipative forces.
2) Energy transfer as heat can only occur between objects whose temperatures differ by an infinitesimal amount.
3) The process must be quasi-static so that the system is always in an equilibrium state (or infinitesimally near an equilibrium state).
Carnot Engine
A Carnot engine is a reversible engine that works between two heat reservoirs.
It operates in a Carnot cycle.
Carnot Cycle
1) A quasi-static isothermal absorption of heat from a hot reservoir.
2) A quasi-static adiabatic expansion to a lower temperature.
3) A quasi-static isothermal release of heat to a cold reservoir at temperature Tc.
4) A quasi-static adiabatic compression back to the original state
Carnot Efficiency
ε = 1 - Qc/Qh = 1 - Tc/Th
Thermodynamic Temperature
The ratio of the thermodynamic temperatures of two reservoirs is defined to be the ratio of the heat released to the heat absorbed by a Carnot engine running between the two reservoirs:
Tc/Th = Qc/Qh
Entropy
Entropy is a measure of the disorder of a system. The difference in entropy between two nearby states is given by dS = dQrev/dT
dQrev = the heat absorbed during a reversible process taking the system from one state to the other
The entropy change of a system can be positive or negative.
Entropy and Loss of Work Capability
During an irreversible process, the entropy of the universe Su increases and an amount of energy:
Wlost = T*ΔSu
becomes unavailable for doing work.
Entropy and Probability
Entropy is related to probability.
A highly ordered system is one of low probability and low entropy.
An isolated system moves toward a state of high probability, low order, and high entropy.
Thermal Expansion
Coefficient of Linear Expansion
α = ΔL / LΔT
OR
ΔL/L = α*ΔT
Thermal Expansion
Coefficient of Volume Expansion
β = ΔV/VΔT = 3α
OR
ΔV/V = ΔT*β
The Van der Waals Equation
The van der Waals equation of state describes the behaviour of real gases over a wide range of temperatures and pressures, taking into account the space occupied by the gas molecules themselves and the attraction of the molecules to one another.
(P + an²/V²) (V - bn) = nRT
Vapour Pressure
Vapour pressure is the pressure at which the liquid and gas phases of a substance are in equilibrium at a given temperature The liquid boils at that temperature for which the external pressure equals the vapour pressure..
The Triple Point
The triple point is the unique temperature and pressure at which the gas, liquid, and solid phases of a substance can coexist in equilibrium.
At temperatures and pressures below the triple point, the liquid phase cannot exist.
Heat Transfer
The three mechanisms by which energy is transferred due to a difference in temperature are conduction, convection and radiation.
Newton’s Law of Cooling
For all mechanisms of heat transfer, if the temperature difference between the object and its surroundings is small, the rate of cooling of the object is approximately proportional to the temperature difference.
Heat Conduction
Current
Rate of conduction of heat is given by:
I = dQ/dt = -kA dT/dx
I = thermal current k = coefficient of thermal conductivity dT/dx = temperature gradient
Heat Conduction
Thermal Resistance
ΔT = IR
ΔT = temperature decrease in the direction of the thermal current R = thermal resistance
R = |Δx| / kA
Heat Conduction
Equivalent Resistance in Series and Parallel
series: Req = R1 + R2 + …
parallel: 1/Req = 1/R1 + 1/R2 + …
Heat Conduction
R Factor
The R factor is the thermal resistance in units of
inft²F/(Btu/h) for a square foot of a slab of material
Rf = Rnet*A = |Δx|/k
Thermal Radiation
Rate of Radiated Power
Pr = eσAT^4
σ = Stefan's constant = 5.67x10^(-8) W/m²*K^4 e = emmisivity, varies between 0 and 1 depending on the composition of the object
Materials that are good heat absorbers are also good radiators.
Thermal Radiation
Net Power Radiated by an Object to it’s Environment
Pnet = eσA (T^4 - T0^4)
T = object temperature T0 = surrounding temperature A = object surface area
Thermal Radiation
Black Body
A blackbody has an emissivity of 1. It is a perfect radiator, and it absorbs all radiation incident upon it.
Thermal Radiation
Wien’s Law
The power spectrum of electromagnetic energy radiated by a blackbody has a maximum at a wavelength λmax, which varies inversely with the absolute temperature of the body:
λmax = 2.898 mm*K / T