Heat TransferThere are 3 ways that heat can move from one place to another:

conduction

convection

radiation

Heat will travel in just one direction: out of _____________ and into __________

In physics, “cold” does not flow. Heat flows out of something; cold does not flow into it.

H = the Rate of Heat Flow through a conductor

H = Q/T = k A T

d

Unit:

Joules/sec or Watts

Thermal Conductivitythickness

Cross-sectional area

Temperature difference

H = Q/T = k A T d

Let’s try a sample problem using:

A steel slab 5 cm thick is used as a firewall, measuring 3 m x 4 m. If a fire burns at 800 C on one side of a wall, how fast will heat flow through the metal door. (The conductivity of steel is 46 Watts/m•K)

Heating a gas in a fixed volume (isochorically) will increase the gas’..

……temperature (speed of molecules) … and……

…pressure (the force per unit area that molecules hit the walls of the container)

If the walls are not fixed, heating will cause expansion. All three variables are in play:

PV PV T T

=

Often, processes are done in controlled ways keeping one of these variables constant:

isochoric = constant volume P/T = P/T (sealed box)

isobaric = constant pressure (like movable top at 1 atmosphere) V/T = V/T

isothermal = constant temperature (like in an ice bath at 0C or a 100C boiling water bath) PV = PV

In the mid-1800’s

Ludwig Von Boltzmann

came up with a constant to connect micro

phenomena (like molecular speed) that we cannot see or

measure to macro phenomena that we

can measure (like temperature,

volume and pressure) for ideal gases.

In the mid-1800’s Ludwig Von Boltzmann came up with a constant to connect micro phenomena (like molecular speed) that we cannot see or measure to macro phenomena that we can measure (like temperature, volume and pressure) for ideal gases.

KEavg = 3/2 k BT

PV = N k B T

vrms = 3 k B T/

k B =

Boltzmann’s constant

1.3 x 10–23 J/K

Root mean square

Velocity of molecules

Remember, these equations only work if T is in Kelvin degrees

Avagodro’s #

6.02 x 1023

molecules/mole

The mass of 1 molecule

These equations work for the majority of gases (called ideal gases) because most gas molecules don’t have intermolecular attractions. Two important exceptions are the non-ideal gases steam and ammonia, where molecules attract due to hydrogen bonding, since O and N are so electronegative.

Lets practice using these equations:

KEavg = 3/2 k BT

PV = N k B T

vrms = 3 k B T/

Find of the speed of an average nitrogen molecule in the air at STP?

What about an oxygen molecule under the same conditions?

What would both their kinetic energies be?

How much volume would 1 mole of air occupy?

Before Boltzmann’s constant, a gas constant R was used, where R = 8.31 J/mole K

KEavg = 3/2 k BT

PV = N k B T

vrms = 3 k B T/

In reality, k B = R(n/N)Avagodro’s #

6.02 x 1023

molecules/mole

# of moles in sample

PV = nR T

vrms = 3 R T/M

Molar mass

Amadeo Avogadro

Lets practice using these equations: PV = nR T

vrms = 3 R T/MUnder what pressure will 1 mole of hydrogen gas occupy 30 liters at 0 C?

How fast will those H molecules be moving at this temperature?

The calorie had been defined as the amount of heat it takes to raise the temperature of 1 gram of water by 1 degree C.

James Prescott Joule use his device below to find out how much work you would have to do to create a calorie of heat.

Work done by falling weights

= mghThe Mechanical

Equivalent of Heat was found to be 4.2

Joules of mechanical work per calorie of

heat produced

4.2 J/cal

A typical AP problem using the mechanical

equivalent of heatA man does 300 Joules of work on a gas.

How many calories of heat has he added?

A 10 kg cinder block is dropped 50 meters. How many calories of heat will it develop if dropped into 1000 kg water?

Pool of water Pool of water Pool of water

SAT2: How much will the water’s temperature go up?

Adding pressure to gas under a pistonBefore weights were added, assume the gas was at normal atmospheric pressure , 1.01 x 105 Pa. Calculate the new pressure in each case, if the added masses are each 10 kg. Given: the pistons dimension are 0.25 m x 0.25 m.

P = F/A + P0Each weight adds W = mg = 100 N

Area = 0.25 m x 0.25 m

= 6.25 x 10 –2 m2

So each weight adds F/A

= 100N / 6.25 x 10 –2 m2

= 1600 Pa = + 1.6 kPa

101 kPa +1.6 kPa

=102.6 kPa

=104.2 kPa

= 105.8 kPa

Could we use any of these equations to figure out the speed of vibrating molecules in a solid and different temperatures and pressures?

No. They work for ideal gases only. The assumptions in their derivations are that there are no attractions between molecules and that they just bounce elastically off one another. This is not true of solids or liquids.