Semester 1: Questions Flashcards
Define thermodynamics
Relations between macroscopic quantities, such as heat and other forms of energy, without understanding the statistical origin.
Define statistical physics
The explanation of thermodynamic laws, requiring the use of thermodynamic relationships in order to explain the physics.
Define vulcanisation
The curing of elastomers, such as latex, into solid rubber.
What is a system?
Whatever part of the universe we choose to study.
What is the surrounding?
Parts of the universe that are not chosen to study.
What is a phase?
A region within a system that is homogeneous and has well defined boundaries.
What is a closed system?
When there is no particle exchange between the system and surroundings.
What is an adiathermal system?
No heat exchange allowed between the system and surrounding (a thermally isolated system).
What is an adiabatic system?
An adiathermal and reversible system (often used synonymously with adiathermal).
Define isothermal
A constant temperature.
Define isobaric
A constant pressure.
Define isovolumic
A constant volume.
Define equilibrium
A state without apparent change. For example, a cease of heat flow refers to thermal equilibrium and fixed boundaries refers to mechanical equilibrium. Equilibrium allows functions of state to be defined.
What is a function of state?
Any quantity that has a well defined value for each equilibrium state (not including microscopic quantities such as particle velocity). In thermodynamics these are often referred to as thermodynamic functions, thermodynamic coordinates, or thermodynamic variables.
What is an extensive function of state (with examples)?
A function of state that is proportional to the system size. Examples: energy, volume, and magnetisation.
What is an intensive function of state (with examples)?
A function of state that is independent of the size of the system. Examples: temperature, pressure, and magnetic field.
Are microscopic quantities functions of state? Why?
They aren’t because they vary even when the system is in equilibrium.
Give two examples of properties that aren’t functions of state. Why aren’t they functions of state?
- Work done
- Heat transferred
These properties depend on the process that causes the energy transfer as well as the states involved.
Define the zero-th law of thermodynamics
Two systems in thermal equilibrium with a third are also in thermal equilibrium with each other.
What is the equation that relates temperature in Fahrenheit to temperature in Celsius?
F = temperature in Fahrenheit
C = temperature in Celsius
What is a thermometer?
An instrument for measuring and indicating temperature, typically designed based on thermal expansion.
Who developed the 3 types of thermometers?
- Galileo Galilei
- Daniel Gabriel Fahrenheit
- Anders Celsius
How does the Galilei thermometer work?
Air is trapped in a cylinder that floats or sinks in liquid depending on its temperature.
How does the Fahrenheit thermometer work?
It is a refined version of the Galilei thermometer that uses glass tubes and the Fahrenheit temperature scale.
How does the Celsius thermometer work?
Modern thermometers use this model, where the temperature scale is decimalised with 0ºC being the freezing point of water and 100ºC being the boiling point.
What is the ideal gas equation?
p = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
What is the equation that relates temperature in Kelvin to temperature in Celsius?
K = Kelvin
ºC = Celsius
What is an equation of state?
An equation that relates different thermodynamic functions to one another. These are generally given the notation f(p, V, T, …).
What are degrees of freedom?
The number of independent parameters that define the state of a system.
What is redundancy?
The statistical effect of having more functions of state than independent variables; it occurs due to the existence of equations of state.
What is the form of a partial derivative for x = x(y, z)?
What is the equation for the reciprocal theorem?
How can the reciprocal theorem be derived?
1) Calculate the partial differentials of two equations x = x(y, z) and z = z(x, y).
2) Substitute the partial differential of z = z(x, y) into that of x = x(y, z).
3) The coefficients of dx must be equal to 1 and those for dy must be equal to 0 so the dx coefficients can be rearranged to find the reciprocal theorem.
What is the equation for the reciprocity theorem?
How can the reciprocity theorem be derived?
1) Calculate the partial differentials of two equations x = x(y, z) and z = z(x, y).
2) Substitute the partial differential of z = z(x, y) into that of x = x(y, z).
3) The coefficients of dx must be equal to 1 and those for dy must be equal to 0 so the dy coefficients can be rearranged to find the reciprocity theorem.
A differential is exact if it is ______ and _____ ______ everywhere.
Finite
Single valued
What equation can be used to prove that a function, f = f(y, z), is single-valued?
Given that df = Y(y, z)dy + Z(y, z)dz, the following must be true:
All functions of state are _____ ______ so have exact differentials.
Single valued
Define the first law of thermodynamics
Energy is conserved if heat is taken into account.
How can the first law of thermodynamics be expressed mathematically?
∆E = sum of work done on the system
∆W = work done to the system
∆Q = heat supplied to the system
Define heat supplied to a system
The energy entering a system through means other than work done, represented by the symbol ∆Q.
What is the equation for the first law of thermodynamics when changes are infinitesimal?
dE = đW + đQ = -pđV + đQ
đW = -pdV = mechanical work done
đQ = heat supplied
Define heat capacity
The heat energy required per unit increase in the temperature of a system.
What is the equation for heat capacity?
C = heat capacity
đQ = change in heat energy
dT = change in temperature
How can the equation for heat capacity be derived?
1) Calculate the exact differential of energy with respect to temperature and volume, given that they are independent.
2) Substitute this into the inexact differential for heat supplied.
3) Divide this differential by the change in temperature to give heat capacity.
Define specific heat capacity
The heat capacity per unit mass of the system, usually represented by the symbol, c. Specific heat capacity has the units J/K/kg.
What is the equation for isovolumic heat capacity?
Cᵥ = isovolumic heat capacity
đQ = change in heat energy
dT, ∂T = change in temperature
∂E = change in energy
What is the equation for isobaric heat capacity?
Cₚ = isobaric heat capacity
đQ = change in heat energy
dT, ∂T = change in temperature
∂E = change in energy
∂V = change in volume
p = pressure
What is the equation for the difference between isobaric and isovolumic heat capacity?
Cᵥ = isovolumic heat capacity
Cₚ = isobaric heat capacity
∂E = change in energy
∂V = change in volume
∂T = change in temperature
p = pressure
What is the adiabatic index?
The ratio between isobaric and isovolumic heat capacities for an ideal gas (as E is only a function of T for an ideal gas).
What is the equation for the adiabatic index?
γ = adiabatic index
Cᵥ = isovolumic heat capacity
Cₚ = isobaric heat capacity
R = gas constant
How can the equation for the adiabatic index be derived?
1) Rewrite the ideal gas equation with the knowledge that the internal energy has no dependence on volume (so ∂V/∂T = R/p).
2) Substitute this into the equation for the difference between isobaric and isovolumic heat capacity.
3) Calculate the ratio between these two heat capacities.
What is the adiabatic index for a monoatomic (or ideal) gas?
Cᵥ = isovolumic heat capacity
Cₚ = isobaric heat capacity
What is the adiabatic index for a diatomic gas?
Cᵥ = isovolumic heat capacity
Cₚ = isobaric heat capacity
What are the two types of expansion of 1 mole of an ideal gas?
- Isothermal expansion
- Adiabatic expansion
Describe isothermal expansion
Isothermal expansion occurs when temperature is constant. From the first law, this menas that heat must be supplied to expand an ideal gas from one volume to another at a fixed temperature.
What is the equation for isothermal expansion?
∆Q = heat supplied
p = pressure
R = gas constant
T = temperature
V₁ = initial volume
V₂ = final volume
Describe adiabatic expansion
Expansion that occurs when no heat is exchanged (so đQ = 0).
What is the equation for adiabatic expansion?
T = temperature
V = volume
p = pressure
γ = adiabatic index
How can the equation for adiabatic expansion be derived?
1) As no heat is exchanged, dE = dW = -pdV from the first law of thermodynamics.
2) For an ideal gas, dE = CᵥdT and pV = RT.
3) Substitute the ideal gas equations into the equation for the first law.
4) Take logs of either side and rearrange.
What is the shape of a p-V plot for adiabats and isotherms?
What is a reversible process?
A process that occurs infinitely slowly so that the system goes through an infinite sequence of equilibrium states (which are infinitely close together). This must occur without friction, turbulence, acceleration, or anything else that results in an imbalance of forces. This is often referred to as a quasistatic process.
What is an irreversible process?
A process that has asymmetry in time due to an imbalance of forces within the system.
Give an example of an irreversible process
Joule expansion
Define joule expansion
The irreversible expansion of gas into a vacuum upon the sudden lifting of a partition. It is irreversible due to the large number of gas molecules.
The ______ law of thermodynamics is the only law in the entirety of Physics/Science that is time-irreversible.
Second
Define the second law of thermodynamics
Heat always moves from hotter objects to colder objects, unless energy is supplied to reverse the direction of heat flow. Hence, the total entropy of a system either increases or remains constant in any spontaneous process; it never decreases.
What is the Kelvin definition of the second law of thermodynamics?
No process is possible whose sole result is the complete conversion of heat into work.
What is the Clausius definition of the second law of thermodynamics?
No process is possible whose sole result is the transfer of heat from a colder to a hotter body.
What is a heat engine?
A system in which a working substance (usually an ideal gas) is used cyclically. It interacts with two heat reservoirs at different temperatures; heat is obtained from the hotter reservoir and work is done to pass some of it to the cooler reservoir.
Given example of a heat engine
The Carnot cycle
Describe the process of the Carnot cycle
A heat engine is formed that consists of 2 isotherms and 2 adiabats. In this engine, reversible processes can occur in this order:
1) Isothermal expansion
2) Adiabatic expansion
3) Isothermal compression
4) Adiabatic compression
How can the total work done in the Carnot cycle be calculated?
By calculating the area enclosed by a p-V graph for 2 isotherms and 2 adiabats.
What is the equation for the work done by a heat engine (using the first law of thermodynamics)?
W = work done by the system
Qₕ = heat absorbed by the system
Qₗ = heat released by the system
What is a heat pump?
A heat engine in reverse. This means that heat is extracted from a lower temperature and delivered to a higher temperature, like a refrigerator.
At what part of the Carnot cycle is work done by the system and heat is absorbed?
Isothermal expansion
At what part of the Carnot cycle is work done by the system and no heat is exchanged?
Adiabatic expansion
At what part of the Carnot cycle is work done on the system and heat is released?
Isothermal compression
At what part of the Carnot cycle is work done on the system and no heat exchanged?
Adiabatic compression
What is the equation for heat absorbed by the system during isothermal expansion in the Carnot cycle?
Qₕ = heat absorbed
What is the equation for the temperature difference during adiabatic expansion in the Carnot cycle?
Tₕ = higher temperature
Tₗ = lower temperature
What is the equation for heat released by the system during isothermal compression in the Carnot cycle?
Qₗ = heat released
What is the equation for the temperature difference during adiabatic compression in the Carnot cycle?
Tₗ = lower temperature
Tₕ = higher temperature
What is the equation for ratio between heat absorbed by the system and heat supplied by the system (using the 4 Carnot cycle equations)?
Qₕ = heat absorbed by system
Qₗ = heat supplied by system
Tₕ = higher temperature
Tₗ = lower temperature
What is the equation for the efficiency of a Carnot engine?
η = efficiency
W = work done
Qₕ = heat absorbed by system
What is the equation for the efficiency of a heat pump (refrigerator)?
η = efficiency
W = work done
Qₗ = heat supplied by system
Describe a Carnot engine (as a diagram)
Describe a Carnot refrigerator (as a diagram)
Define Carnot’s theorem
Of all heat engines working between two given temperatures, none is more efficient than a Carnot engine.
How can Carnot’s theory be proven?
By contradiction. Suppose there was an engine more efficient than the Carnot engine; this engine could be used to drive the Carnot engine in reverse so the net effect would be to transfer an amount of heat from cold to hot. This violates Clausius’ statement of the second law.
Define the corollary of Carnot’s theorem
All reversible engines have the same efficiency as that of a Carnot engine.
How can the corollary of Carnot’s theorem be proven?
By contradiction. Suppose there was a reversible engine less efficient than the Carnot engine; the Carnot engine could be used to drive this engine in reverse so the net effect would be to transfer an amount of heat from cold to hot. This violates Clausius’ statement of the second law.
What does Carnot’s theorem prove?
It proves that the Kelvin statement and the Clausius statement of the second law of thermodynamics are equivalent.
What is thermodynamic temperature?
A definition of temperature that is not dependent on any material property. Instead it used reference temperature and compares the amount of heat exchanged.
How is thermodynamic temperature defined using heat engines?
1) Pick a reference temperature, x₁.
2) Measure another temperature, x₂, by running a reversible heat engine between the two temperatures and comparing the amount of heat exchanged: x₂ = x₁ * Q₂/Q₁.
What is Maxwell’s Demon?
A thought experiment in which a hypothetical intelligent being is capable of detecting and reacting to the motion of every individual molecule in a system. For Joule expansion, this ‘demon’ could control the partition so that only high energy molecules can pass through the partition and low energy molecules remain on the original side. This would raise the temperature in the high energy chamber and lower it in the low energy chamber which is a violation of the second law of thermodynamics.
Define entropy
A thermodynamic quantity/function of thermodynamic variables that measures how much of a system’s energy per unit temperature is unavailable for doing useful (mechanical) work, often referred to as a systems degree of disorder.
What are the two equations that represent the thermodynamic definition of entropy?
dS = change in entropy
S = entropy
đQ = change in heat energy
What is the equation for entropy for 1 mole of an ideal gas?
đQ = change in heat energy
T = temperature
R = gas constant
V = volume
How can the equation for entropy be applied to an ideal gas?
1) Divide the first law of thermodynamics by T so that the LHS represents entropy.
2) Rewrite the equation, knowing that E = 3RT/2 and pV = RT.
3) Replace dT/T and dV/V with d(lnT) and d(lnV).
What is the equation for the Clausius inequality?
T = temperature of external heat reservoir
đQ = change in heat energy
Define the Clausius inequality
For an irreversible process, the heat entering the system at any point in the cycle must be less than or equal to zero.
What does the Clausius inequality say about the entropy of a system?
The change in entropy of a system must always be greater or equal to 0.
Define the law of increase in entropy
The entropy of an isolated system tends to a maximum.
What is the equation for the change in entropy when heat is passed from one object at a given temperature to another at a different temperature?
Write the first law of thermodynamics in terms of entropy
What are the Maxwell relations for the first law of thermodynamics?