physics - temperature, ideal gases & thermodynamics

Thermal Energy Transfer

Thermal Energy is transferred from a region of higher temperature to an area of lower temperature

Thermal Equilibrium

When there is no net transfer of energy between regions, and both regions reach an equal temperature

How is temperature measured?

Temperature is measured using a physical quantity that varies with temperature

Examples of Temperature Measure Methods

• Density of a Liquid: Thin glass capillary tube contains a liquid that expands with temperature, scale measures length of liquid in column. Calibrated at 0 and 100degC

• Volume of Gas at Constant Pressure: As T increases, V increases as at constant P T is proportional to V. Calibrated when temp of gas at a certain volume is known

• Resistance of a Metal

• emf of a Thermocouple: Thermocouple is used as a sensor in thermometers, two different metals connected, creating two junctions with a temp difference. Greater temp diff means greater emf

Thermodynamic Temperature Scale

The Kelvin Scale: Does not depend on physical property of a substance
K = T+273.15
Lowest possible temperature: Absolute 0, 0K, where average KE of molecules is at a minimum

Specific Heat Capacity

The amount of energy required to raise the temperature of 1kg of a substance by 1degC
Q=mc deltaT

Specific Latent Heat

The thermal energy required to change the state of 1kg of a substance with no change in temperature
Q=mL

Specific Latent Heat of Fusion

The thermal energy required to change the state of 1kg of a substance from solid to liquid with no change in temperature

Specific Latent Heat of Vaporisation

The thermal energy required to change the state of 1kg of a substance from liquid to gas with no change in temperature

Mole

Amount of substance containing the same number of molecules as there are in 12g of Carbon-12
n=N/NA=m/Mr

Ideal Gas at constant Pressure

Volume is proportional to Temperature
Increased Temp means particles have increased average KE so move further apart, increasing volume

Ideal Gas at Constant Volume

Pressure is proportional to Temperature
Increased temperature means particles have increased average KE, collide more so exert more force, increasing pressure

Ideal Gas at Constant Temperature

Volume is inversely proportional to pressure
In a smaller volume, more collisions, more force exerted so higher pressure

Ideal Gas State Equation

pV=nRT
pV=NkT

Assumptions of Kinetic Theory of Gases (10)

• Molecules behave as identical

• Molecules undergo perfectly elastic collisions

• Molecules are perfectly elastic spheres

• Molecules have negligible volume

• Molecules do not have any attractive/repulsive forces

• External forces are ignored

• Newton’s laws apply

• Molecules are in constant random motion

• Time of a collision is negligible compared to time between collisions

• Large number of molecules

What causes pressure

Molecular movement. When molecules collide with container walls, change in momentum causes force exerted on wall. Many molecules will exert forces on the wall, creating an average overall pressure

Derivation of Pressure

change in momentum = -2mc
Time between collisions = 2l/c
F=2mc/2lc^-1=mc²/l
P=mc²/l³
For N Molecules: P=Nm<c²>/l³
Considering 3D Motion:<c²>=<cx²>+<cy²>+<cz²>
x=y=z
<cx²>=1/3<c²>
P=1/3Nm<c²>/l³
PV=1/3Nm<c²> OR P=1/3rho<c²>

Translational KE

Translational KE = 3/2kT = 1/2m<c²>
The kinetic energy of molecules as determined by their temperature
for N molecules = 3/2NkT

Internal Energy

The sum of the random distribution of potential and kinetic energies of molecules within a system
Relates to temperature

Work done by a gas

W=P deltaV

First Law of Thermodynamics

Based on Conservation of Energy
The increase in internal energy of a system is equal to the sum of thermal energy into the system and the work done on it
deltaU = q + W