Unit 5: Thermodynamics and engines Flashcards
What is thermodynamics?
The study of the relationship between heat and other forms of energy
What do equations of state involve i.e. the three gas laws?
Pressure, volume and temperature
What is Boyle’s law in words?
For a fixed mass of gas at a constant temperature, the product of the pressure and volume is constant
What is the equation for Boyle’s law?
pV = constant or p is proportional to 1/V at constant T
What is Charles’ law in words?
For a fixed mass of gas at constant pressure, the volume is directly proportional to the temperature measured in kelvin
What do gas laws apply only to?
A fixed amount of gas
What is the equation for Charles’ law?
V/T = constant or V is proportional to T at constant p
What is the definition of 1 kelvin?
A temperature change of 1 kelvin is identical to a temperature change of 1°C, the kelvin and celsius scales have equal increments but they start at different places: 0K = -273.15°C
What is the pressure-temperature law in words?
For a fixed mass of gas at constant volume, the pressure is directly proportional to the temperature measured in kelvin
What is the equation for the pressure-temperature law?
p/T = constant or p is proportional to T at constant V
Do real gases obey the gas laws exactly?
No
What do the gas laws give an accurate description of?
The way gases behave at low temperatures and temperatures that are well above their liquefaction temperature
What is the equation for the ideal gas law and what do the terms in it represent?
pV = nRT where V is the volume in m^3, T is the temperature in kelvin, p is gas pressure in Nm^-2 or Pa, R is the universal molar gas constant = 8.31 JK^(-1)mol^(-1) and n is the number of moles
What can be said about a gas that obeys the ideal gas law exactly?
This gas has exactly no forces acting between the molecules and hence the internal energy (energy of molecules) is entirely kinetic and depends only on its temperature
What does the first law of thermodynamics relate?
Heat and work and it is essentially the principle of the conservation of energy
What is the equation for the first law of thermodynamics and what do the terms represent?
Q = ΔU + W where Q is the heat entering the system, ΔU is the increase in internal energy and W is the work done by the system
How can internal energy be increased?
By doing work on the system i.e. compressing it or putting energy into the system
What does the change in internal energy depend on?
The change depends on the initial and final states of the system and not how the change was brought about
What is an isolated system?
A system cut off from any external influence
What are the conditions of an isolated system?
No work can be done hence W = 0, no heat can enter or leave the system hence Q = 0 therefore ΔU = 0 and the internal energy of an isolated system is constant
When do adiabatic process occur?
They occur very rapidly or in a system that is so well insulated that no transfer of energy as heat can occur between the system and its external environment
What is the condition for a adiabatic process?
Q = 0
What does the first law of thermodynamics change to in an adiabatic process?
ΔU = -W
What is the definition of internal energy?
The internal energy of a system is the sum of the kinetic and potential energies of the atoms and molecules comprising the system, the value of the absolute internal energy of a system cannot be measured, only its change from one state into another
What is an isothermal process?
A process that takes place under constant temperature conditions
What is the formula for an isothermal process in terms of pressure and volume?
pV = constant
What is the formula for an isothermal process in terms of the first law of thermodynamics?
Q = W as ΔU = 0
What is necessary if a gas is to maintain its temperature when it expands?
If a gas expands and does external work W, an amount of heat Q has to be supplied to the gas in order to maintain its temperature and vice versa
What is required to produce an isothermal change ?
It requires a gas to be kept in a thin-walled vessel that is composed of an excellent conducting material surrounded by a constant temperature bath - any expansion or contraction within the system must take place slowly, under such conditions the process can be reversed and returned to its initial state i.e. the process is reversible
In practice, is it possible to produce a perfectly reversible change?
No
What is the formula for a reversible isothermal change?
p1V1 = p2V2
What is an adiabatic process?
A process that takes place in such a way that no heat can enter or leave the system
What is the formula for an adiabatic process in terms of pressure and volume and when can this formula be applied?
pV^Ɣ = constant and this formula can be applied when a gas undergoes a reversible adiabatic expansion or contraction
What does Ɣ depend on?
The molecular structure of the gas
What is the formula for Ɣ?
Ɣ = cp/cv
What is the formula for an adiabatic process in terms of the first law of thermodynamics?
W = -ΔU as Q = 0
In an adiabatic process, what happens when a gas expands and does external work?
Its temperature falls and vice versa
Is a truly adiabatic process possible?
No
What processes can produce near-adiabatic conditions?
Processes that can happen suddenly and rapidly such as the rapid expansion and contraction of air when sound waves pass through
What is the formula for an adiabatic process when there are two gases involved for instance?
p1V1^Ɣ = p2V2^Ɣ OR p1V1/T1 = p2V2/T2 OR T1V1^(Ɣ -1) = T2V2^(Ɣ -1)
What are the conditions for constant-volume processes?
The system can do no work if the volume of a system such as a gas is held constant, if heat is absorbed by the system (Q is positive) then the internal energy of the system must increase and vice versa
What is the formula for a constant-volume process in terms of the first law of thermodynamics?
ΔU = Q as W = 0
What is the formula for a constant-volume process in terms of cv?
Q = cvΔT
What is cv?
Cv is the molar heat capacity of a gas at constant volume, it is the heat required to produce unit temperature rise in one mole of the gas when the volume remains constant
What is the external work done by an expansion of a gas at constant pressure?
W = pAΔs where A is the cross-sectional area and Δs is the small distance moved by the piston
What is work done equal to in terms of pressure and volume?
W = pΔV
What is the formula for a constant-pressure process in terms of cp?
Q = cpΔT
What is cp?
Cp is the molar heat capacity of a gas at constant pressure, it is the heat required to produce unit temperature rise in one mole of the gas when the pressure remains constant
What is a restriction and consequence of an isothermal process?
The restriction is that ΔU = 0 and the consequence is that Q = W
What is a restriction and consequence of an adiabatic process?
The restriction is that Q = 0 and the consequence is that W = -ΔU
What is a restriction and consequence of a constant volume process?
The restriction is that W = 0 and the consequence is that ΔU = Q
What is a restriction and consequence of a constant pressure process?
The restriction is that W = pΔV and the consequence is that Q = ΔU + pdV
What is a p-V diagram and what can it also be referred to as?
It is a plot of pressure versus the volume of a gas and it is also known as an indicator diagram
What is the formula for work done in terms of pressure?
It is the integral of p with respect to volume between the initial and final volume
What is represented by the area under a p-V diagram?
The work done
What does the area of a loop represent?
The work done per cycle
Does a gas do work in a compression?
Work is done on the gas in a compression
What is an engine?
A device or system that extracts energy from its environment in the form of heat and converts it into useful work
What is present in every heat engine?
A working substance
What does an internal combustion engine use?
A petrol-air mixture
What does a steam engine use?
Water