Introduction and some key terms Ch1-3 Flashcards
WIA function of state?
A function of state is any physical quantity that has a well defined value for each equilibrium state.
WIA EXTENSIVE function of state. Give examples.
Extensive = Proportional to system size.
Ex = Energy, E, Volume, V
WIA INTENSIVE funtion of state?
Give examples.
Intensive = Independent of size of system.
Ex = pressure, P, Temperature, T
Are microscopic properties such as particle velocities considered functions of state?
NO, neither is work done or heat transferred as they depend on the process and not just the states.
What is the Zero-th law of Thermodynamics?
Zero-th law: If 2 systems are in thermal equilibrium with a third system, then the 2 systems are in thermal equilibrium with each other
Although Ideal gases are impossible, how could we experimentally achieve them?
Speciall case: Use 1 mole of a very dilute gas.
Ideal Gas eq.
pV = nRT
Functions of states are not all independent (otherwise there would be no theory), hence there are equations of state
The most important equation of state is pV=nRT
Functions of states are not all independent (otherwise there would be no theory), hence there are equations of state
The most important equation of state is pV=nRT
3 functions of states, p,V,T, knowing 2 fixes the 3rd, hence ‘2 degrees of freedom’, e.g. you might see T(p,V) or E(p,V)
What is the area under a P/V graph equal to?
Area under P/V curve = Work
(mechanical work)
What is the equation of mechanical work in terms of pressure and volume?
W = p x V
(from W = Fd, F= PxA –> W = PxAxL = pxV)
dw = p x dV
OR
dw = dp x V
Define Adiathermal
No heat exchange allowed- thermally isolated.
dQ = 0 «—- important-
dE = dQ + dW –> dq =0 hence dE = dW
Adiabatic also used to mean Adiathermal, but now is taken to mean isentropic..
Define Isobaric
At constant Pressure
Define Isovolumic
At constant volume
Define Phase
Region within a system that is homogeneous(the same) and with well defined boundaries.
What is the First Law of Thermodynamics? (def)
The first law States that the Internal energy Change of a system, dE, is the sum of the Work done on the system dW and the Heat supplied to the system dQ.
What is first Law of Thermodynamics (eq)
E = Q + W
If a system has done work on its surroundings, then the system has done NEGATIVE work- when an object does work it LOSES energy.
Why is dW = -p dV?
If a system has a reducing volume , then you are doing work on the system(work done on system, dW, is positive). However, dV is negative, so for dW to be positive the negative sign is needed, dW = -p dV (- x - = positive). This works the other way, if the Volume is increasing, the system is doing work on the environment, hence the work done on the system is negative (dW is -ve), so for dw to be negative-» must have dW = - p dV (- x+ = -).
T/F? dE = -p dV + dQ?
T
T/F? dQ = dE + p dV
T
If Energy is a function of Temperature and Volume- E(T, V), how could you express dE?
What is the equation of Heat capacity? What do Cp and Cv refer to?
C = dQ/dT
Cp = Heat capacity at const. pressure PER MOL
Cv = Heat capacity at const. Volume PER MOL
Derive the heat Capacities for const. Volume and for const. pressure using the First law of Thermodynamics.
Hint 1: Use dE = dW + dQ.
Hint 2: Energy is a function of Temp and Vol, E(T, V).
Hint 3: dW = - p dV, C = dQ/dT
How do Specific Heat Capacity and Heat Capacity differ. What is the difference between Cp and Cv?
Heat Capacity is the amount of thermal energy needed to change a substance’s temperature by 1 K (or degree). Specific heat capacity is the amount of energy required to change a substance’s temperature by 1 K per unit kilogram.
SHC = HC/m
Cp-Cv = R/n Cp and Cv are molar heat capacities! Don’t forget this!
n*(Cp - Cv) = R
Derive an equation for the adiabatic constant using equations for Cp and Cv - assuming ideal gas (dE/dV) = 0.
Derive change in thermal energy the Isothermal expansion of 1 mole of ideal gas.
Hint: Internal energy (E) and Temp. (T) remain const. dE = dQ + dW -»> dQ = -dW (dE = 0)
Isothermic expansion: Thermal Energy Q drawn from surroundings to maintain const. Temp.
Isothermic compression: Thermal Energy Q released to surroundings “ “.
Derive the equation of an ideal gas for an adiabatic process
State the equations of Ideal gas for Isothermal and Adiabatic processes.
Why does adiabatic compression require more work than isothermal compression?
With adiabatic compression, work is done increasing the pressure, as well as the Temperature and Internal Energy of the system, where as with isothermal compression, work is only done to increase the pressure of the system, not the E or Temp.
Def Reversible Process
A reversible process is a process carried out so slowly that the system goes through an infinite sequence of equilibium states (which are infinitely close together).
What must a reversible process be absent of?
Absent of fricition, turbulence, or acceleration.
What is the Second Law of thermodynamics?
The entropy of a system ALWAYS increases.
Note the Carnot cycle can be reversed, now the surroundings do work on the system, which extracts heat from a lower Temp and delivers that to a higher Temp.
BE CAREFUL- here W is the work done BY THE SYSTEM and elsewhere in thermodynamics W is the WORK done ON THE SYSTEM- not reversed process in image, if reversed +W + Qh - Ql = 0,
W = Ql -Qh
Describe Each Path A-B-C-D…
A to B- Isothermal expansion, work done by system, heat, Qh absorbed.
B to C- Adiabatic expansion, work done by system, no heat exchange, Temp decrease.
C ot D- Isothermal Compression, work done ON system, heat, Ql released.
D to A- Adiabatic Compression, work done ON system, no heat exchange, Temp increase.
Using the equations of Adiabatic and Isothermal Compression/Expansion, state four equations that link each of the paths.
State the equation of the efficiency of a Carnott Engine (forward process- for reverse change direction of energy flow) (a) in terms of work, (b) in terms of heat and (c) in terms of Temp.
The reason that the Carnot refrig. has Ql/Tl as the numerator is because that is the target Energy/Temperature. The Carnot heat pump has Qh/Th as the numerator as that is the target Energy/Temperature.
What are the Molar heat capacites and adiabatic constants of (a) mono-atomic and (b) Di-atomic gases?
Remember that Cv is a MOLAR constant, so heat capacity is n*Cv
Monoatomic C = 3R/(2n)
Diatomic C = 5R/(2n)
State Carnot’s Theorem. What does this mean for reversible engines?
Of all heat engines working between two temperatures, none is more efficient than a Carnot engine.
ALL reversible engones have the same efficiency as a Carnot engine.
Why can you not have an engine more efficient than a Carnot engine? (What is the combined effect?)
For the efficiency n’(of other) to be greater than the Carnot engine (in this case the Carnot engine is in reverse) then Qh’ is smaller than Qh. Other eng. requires a smaller heat input Qh’, as a result, produces less heat as a result, dumps less heat Ql’ into the lower Temp.
Looking at this as a whole, we see that other takes less heat from Th than it would pump into Tl, and Carnot takes more heat from Tl and pumps it to Th.
Net result is heat being pumped from cold to hot which violates 2nd Law.
How is Thermodynamic Temperature defined?
- Choose reference temperature theta1
- Measure any temperature by running a heat engine between the reference temperature and measured temperature.
- The amount of heat exchange defines theta2
How is Empirical Temperature Defined?
- Using a thermometer
- Measurement depends on material properties
- Using ‘ideal gas’ temperature scale.
How is Thermodynamic Temperature defined?
Defined on the notion of reversibility and through thr carnot theorem in that all reversible heat engines have the same efficiency, so can define temperature scale.
Why do all reversible engines have the same efficiency as that of a Carnot engine
Use proof by contradiction, draw diagram, similar to card 39/carnot cycle being the most efficient engine proof.
