Thermal Physics

Thermal Physics

• Thermodynamics:
• Thermodynamics is the study of energy & its effects on a system.
• Heat & Temperature:
• Temperature is a measure of the K.E of its molecules. Temperature indicates in which direction heat will flow when 2 bodies are placed close together.
• Heat is the thermal energy transferred from a body at a higher temperature to a body at lower temperature due solely to the temperature difference in Joules.

Internal Energy

• 
• Internal energy is defined as the sum of all the kinetic & potential energies of the molecules within a substance. It's represented by the Symbol U.
• Potential Energy: changes as molecules gets squeezed closer together & move further apart.
• The moving molecules in water, for example, have kinetic energy but their movement is disorganised-it changes all the time, randomly.
• Equation for Internal Energy:
• U= Kinetic energy of molecules + Potential energy of molecules (bonds)

Absolute 0 & the Kelvin temperature

• The Celsius scale starts at the freezing point of water- this isn't the fundamental temperature: it was chosen for convenience.
• There's a more important & fundamental temperature at -273℃- this is the absolute 0 of temperature
• Absolute 0 is the temperature at which the internal energy of any system at the lowest possible value. It can't cool a system that can't lose internal energy. It's the lowest possible value.
• Absolute temperature doesn't rely on changes in the property of a substance due to temperature. It's measured in Kelvin (K).

Specific heat capacity

• For a substance being heated, the rise in temperature depends on the mass of the substance being heated & how much energy has been put in.
• It also depends on what the substance is. In fact:
• -change in internal energy, ΔU= mass*specific heat capacity *ΔT.
• -Equation can also be written as ΔQ(E)=mc ΔT
• Specific heat capacity depends on the substance
• Specific heat capacity definition:
• -The specific heat capacity is the energy needed to raise the temperature of 1kg by 1K (or 1 ℃).
• 

Measuring Specific heat capacity

• A 60 W immersion heater was used in the experiment
• Beaker contained a kg of water at 21℃. After 5 minutes, the heater was switched off.
• The temperature of water went up to 25℃
• Result was too large
• https://www.youtube.com/watch?v=JuWtBR-rDQk (Embed)

Energy loss in measuring heat capacity

• why is the result so large?
• Not all the energy from the electrical heater go to increase the thermal energy of water, because some heat will have escaped to increase the internal energy of the room.
• There's also the apparatus-their internal energies have all gone up
• The increase in the internal energy must be less.

Boyle's Law

• What's the relationship between pressure & volume?
• The volume changes as pressure changes for a sample of gas at a constant temperature. If you double the volume, the pressure halves.
• This is Boyle's law
• -For a fixed mass of gas, at a constant temperature
• -Pressure p is inversely proportional to volume V
• -P1V1=P2V2
• https://www.youtube.com/watch?v=BxUS1K7xu30 (Embed)

Boyle's law

Pressure Law

• 
• The graph shows that the pressure of a fixed mass of gas at a constant volume is directly proportional to temperature.
• This is pressure law: p ∝ volume if the volume is constant.
• Caption: Pressure Law Graph

Pressure Law equation

• 
• Caption: Pressure law equation

Charles Law

• What happens if you keep only pressure constant?
• If you let a gas expand, so that the pressure stays constant, then the volume goes up in direct proportions to the absolute temperatures.
• From this it follows that:
• -Volume is directly proportional to temperature.
• 
• Caption: Charles Law

Charles law graph

• 
• Caption: Charles law graph

Ideal gases:

• An ideal gas is one that obeys Boyle's law under all conditions however, in reality, no real gas is an ideal gas under all conditions.
• Under conditions of low pressure & high temperatures, real gases will obey Boyle's Law & are said to be behaving in an ideal manner.

Ideal gas assumptions

• When describing an ideal gas, the following assumptions are made:
• The molecules have zero size
• molecules are identical
• molecules collide with each other and the walls of their containers without any loss of energy, in collisions which take zero time-elastic collision
• The molecules exert no forces on each other except during collisions
• there are enough molecules so that statistics can be applied.
• Newton's law of motions apply
• Molecules take up eligible volume
• Motion of all molecules is random
• All molecules travel in a straight line
• Internal energy of gas is kinetic energy
• Gravitational and electrostatic forces can be ignored

Ideal gas equation

• 
• What happens if you change the pressure & the volume & the temperature of a sample of gas?
• If you increase the temperature of the gas that would make the volume increase but if you increase pressure then Boyle's law predicts that the volume would decrease.
• To predict what happens when all 3 variables change, you need to use the ideal gas equation:
• PressurexVolume=nXa constant Rx Temperature
• PV=nRT

Kinetic Theory

• Kinetic theory
• -Kinetic theory is about the movement of gas molecules
• Moving particles & gas pressure:
• -Kinetic theory of gases links the macroscopic behaviour of gas with its microscopic behaviour.
• How does Kinetic theory accounts for pressure?
• -For example, the molecule is heading for the wall & it has rebounded, going away from the wall.
• -This is because the wall has decelerated the molecule to a stop & then accelerated in the opposite direction to the same speed. The walls of the box has pushed the particles to the right to produce the acceleration & so the molecules must have pushed the walls to the left with the same force (Newton's 3rd Law)
• - The more massive a molecule is, the larger the force however the acceleration is the same.
• -When a faster molecule collides & rebounds, the change in velocity is greater which means the molecule accelerates more when it rebounds & so needs a larger force.
• - Pressure of a gas in a given volume depends on 3 factors: -mass of molecules
• -speed of molecules (speed^2)
• -how many molecules there are in the container.

Root mean square speed

• At constant temperature the speed of a particle won't remain the same as it'll change as it collides with other particles.
• However, the distribution of speed will remain the same as will average speed. This is the sum of all the speeds divided by the total number of particles.
• The root mean square of the molecules is different from the average speed.
• 

Kinetic theory equation

• -For an ideal gas, the kinetic theory equation is:
• pV=⅓NMC(rms)^2
• 

Kinetic theory model assumptions

• -The kinetic theory equation requires certain assumptions to be made about gas particles:
• -particles move in constant, random motion
• -particles have eligible volume
• -all collisions between particles and the walls of the containers are completely elastic
• - Duration of each collision is much less than the time between collisions
• -Gravitational & electrostatic forces are negligible.

Kinetic Energy&Boltzman constant K

• 
• The theoretical equation for an ideal gas & the ideal gas equation both give you an equation with pV as its subject.
• For 1 mole of gas, pV=⅓ Nmc(rms)^2 & pV=RT
• You can combine to give the equations on the right.
• K is the boltzsman constant
• This is the gas constant R divided by Avogadro constant N. Boltzman Constant: K=R/N
• But ½mc^2 is the mean kinetic energy of a gas molecule, so:
• Mean K.E of a gas molecule(J)= 3/2 x Boltzman constant x temperature (measured in Kelvin)