Topic 2 Flashcards
What is heat capacity?
The heat capacity of a system is the amount of heat that must be supplied to raise its temperature by 1 K.
Heat supplied is path dependent because the heat supplied is not a function of state.
Derive the heat capacity equation
πΆ_πβπΆ_π=ππ = ππ_B
What is the principle of equipartition of energy?
Each independent degree of freedom (quadratic energy term) contributes an amount 1/2 π_π΅ π to the total thermal energy.
(thermal energy is
shared equally by each independent energy storage term.)
What is the total thermal energy of a monoatomic ideal gas?
3/2 π_π΅ π=3/2nRT
What is the heat capacity of a monatomic ideal gas ?
πΆ_π=πΆ_π +nR = 5/2nR
πΆ_π=3/2nR
What is the heat capacity of a diatomic ideal gas ?
πΆ_π=πΆ_π +nR = 7/2nR
πΆ_π=5/2nR( for moderate temp)( for high its 7/2)
How many degrees of freedom does a diatomic ideal gas have and what are they?
Diatomic gases have
3 translational degrees of freedom (translational kinetic energy in each x,
y and z),
2 rotational degrees of freedom (rotational kinetic energy term)
and 1 vibrational degree of freedom (vibrational kinetic
energy ). Vibrational degrees of freedom are often
βfrozen outβ apart from at very high temperatures.
Why doesnβt the rotation around the x axis not contribute for rotational kinetic energy?
Rotation around the x axis does not contribute because we assume that the atoms are effectively point particles.
What is the heat capacity of a solid?
πΆ_π =3R
How many degrees of freedom does a solid have?
Each atom has 3 translational and 3
vibrational degrees of freedom
What is a heat engine?
A heat engine is any device that transforms heat partly into work or mechanical energy
What are reversible processes?
A process is carried out very slowly, so that the gas remains in equilibrium at all times.
What are irreversible processes?
Processes that involve rapid change.
How do you change the state of a gas?
Using different paths: adabatic, isobaric,isochoric and isothermal
What is a isothermal process?
Isothermal processes occur at constant temperature. This follows a curve on a pV diagram
What is a isobaric process?
Isobaric processes occur at constant pressure. This follows a horizontal line in a pV diagram
What is a isochoric process?
Isochric processes occur at constant volume so there is no work
done, βW = 0. This follows a vertical line on a pV diagram
What is a adiabatic process?
Adiabatic processes occur without transfer of heat i.e. βQ = 0
NO HEAT IN OR OUT
What is the thermal efficiency of a heat engine?
Ξ· =W/QH= 1 β|QC|/ QH
Explain the steps of the Carnot Cycle?
1-2 isothermal expansion
2-3 adiabatic expansion
3-4 isothermal compression
4-1 adiabatic compression
Explain the steps of the Otto Cycle?
0-0' 1-2 adiabatic 2-3 isothermal 3-4 adiabatic 4-5 isothermal
What is a reversible heat engine and what are the applications?
A heat engine running backwards transfers heat from a cool reservoir to a hotter reservoir by doing work
Two main applications:
Refrigerators
Heat pumps
What is the equation for the thermal energy of a gas?
U=fnRT/2=fNkbT/2
Why more heat would be required under conditions of constant pressure than constant volume?
Cp > CV because a gas-heated at constant pressure will expand, and when it expands it does work, so you have to put in more energy.