Thermal Energy Transfer, Internal Energy, and Gas Laws in Physics

When does energy transfer take place between objects?

1. An object does work on another by exerting a force

2. Energy is transferred by conduction, convection or radiation due to temperature difference

Internal energy

Energy of molecules due to individual movements and positions

How might internal energy increase?

1. Energy is transferred by heating

2. Work is done

When might internal energy remain constant?

1. No heating or work done

2. Heating and work done balance each other

The change in internal energy of the object is equal to

the total energy transfer due to work done and heating

Internal Energy

the sum of the random distribution of the kinetic and potential energies of its molecules.

How are solids arranged?

Strong forces of attraction between molecules's protons and electron hold atoms in regular lattice Atoms vibrate randomly in fixed positions

How are atoms in liquids arranged?

molecules move about at random in contact with each other forces between the molecules are not strong enough to hold the molecules in fixed positions

How are atoms in gases arranged?

Atoms move in random directions in random speeds

thermal equilibrium

equal temperature

What is the Celsius scale defined as?

1. Ice point, 0oC- pure melting ice

2. Steam point, 100oC- steam

What is the absolute scale defined as?

1. Absolute zero, 0K- lowest possible temperature

2. Triple point of water, 273.16K- ice, water, and water vapour co-exist in thermodynamic equilibrium

An object at absolute zero has _____________ internal energy

minimum

If the pressure measured ac ice point and at steam point is plotted on a graph, the line between the two points always cuts the temperature axis at ______________, regardless of which gas is used or how much gas is used .

-273oC

Specific heat capacity

Energy needed to raise the temperature of 1kg of a substance by 1K without changing state

How can you measure specific heat capacity using an inversion tube?

1. Temperature of the tube is measured before inversion and after a number of inversions

2. The loss in gravitational energy of the lead can be modelled as mgLn where L is length of tube and n is number of inversions

3. mcT = mgLn

How does measuring speific heat capacity using inversion tube work?

gravitational potential energy of the object falling in the tube is converted to internal energy

How can you measure the specific heat capacity of a metal using a metal block?

A block of the metal of known mass in an insulated container is used.

An electrical heater is inserted inro a hole drilled in the metal and used to heat the metal by supplying a measured amount of electrical energy.

A thermometer inserted into a second hole drilled in the metal is used to measure the temperature rise.

Measure the current and voltage every 1 minute.

How can you measure the energy supplied to the heater?

E= Current x pd x time

How can you improve the thermal constact between the thermometer and the metal?

small amount of water since water is a better conductor that air

How can you measure the specific heat capacity of a liquid?

A known mass of the liquid is used in an insulated calorimeter of known mass and known specific heat capacity.

A 12 V electrical heater is placed in the liquid and used to heat it directly.

A thermometer inserted into the liquid is used to measure the temperature rise

How can you calculate specific heat capacity of water?

Electrical energy supplied= IVt

Energy heating liquid= m1c1T

Energy heating calirometer= m2c2T

IVt= m1c1T + m2c2T

What is the electrical energy supplied per second equal to in continuous flow heating?

IV= mc x T/t

specific latent heat of fusion

energy needed to change the state of unit mass of the substance from solid to liquid without change of temperature

specific latent heat of vaporisation

energy needed to change the state of unit mass of the substance from liquid to vapour without change of temperature

Equation for latent heat

E= ml

pressure

force per unit area

Boyle's law

pressure of a gas is inversely proportional to its volume at a constant temperature.

Equation for Boyle's law

pV= constant

Charles' Law

The volueme of a gas is directly proportional to its temperature given that pressure does not change.

Equation for Charles' Law

V/T= constant

isothermal

constant temperature

isobaric

Constant pressure

Equation for work done with pressure and volume

Work done = p△V

Pressure Law

The pressure of a gas is directly proportional to the temperature at constant volume.

Equation for Pressure Law

p/T= constant

Brownian motion

The motion of each particle is because it is bombarded unevenly and randomly by individual molecules. The particle therefore experiences forces due to these impacts, which change its magnitude and direction at random.

Ideal gases

Obey Boyle's law

Ideal gas law equation

pV/T= constant

Ideal gas equation

pV= nRT

Ideal gas equation with Boltzmann constant

pV= NkT

root mean square speed

c1, c2 = speeds of individual molecules N= number of molecules

Kinetic theory equation

Assumptions made in deriving kinetic theory equation

Volume of each molecule is negligible compared with volume of gas. Moelcules do not attract eachother.Continual random motion.Elastic collisions.Collisions with surface is shorter than time between impacts.

Mean kinetic energy of a molecule of ideal gas

3/2kT

The total kinetic energy of n m oles of an ideal gas

3/2nRT

internal energy of n moles of ideal gas at T kelvin

3/2nRT