Heat Transfer There are 3 ways that heat can move from one place to another: radiation conduction convection

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 Unit: Joules/sec or Watts H = Q/T = k A T d Temperature difference Thermal Conductivity thickness Cross-sectional area

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 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

(like temperature, volume and pressure) 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.

k B = KEavg = 3/2 k BT vrms = 3 k B T/ 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 Avagodro’s # 6.02 x 1023 molecules/mole Root mean square Velocity of molecules The mass of 1 molecule Remember, these equations only work if T is in Kelvin degrees

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/ Lets practice using these equations: 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 Before Boltzmann’s constant, a gas constant R was used, where R = 8.31 J/mole K In reality, k B = R(n/N) Avagodro’s # 6.02 x 1023 molecules/mole # of moles in sample Amadeo Avogadro KEavg = 3/2 k BT PV = N k B T vrms =  3 k B T/ PV = nR T vrms =  3 R T/M Molar mass

Lets practice using these equations: PV = nR T vrms =  3 R T/M Under 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?

Work done by falling weights = mgh 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 = mgh The 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 heat A man does 300 Joules of work on a gas. How many calories of heat has he added?

SAT2: How much will the water’s temperature go up? A 10 kg cinder block is dropped 50 meters. How many calories of heat will it develop if dropped into 1000 kg water? SAT2: How much will the water’s temperature go up? Pool of water Pool of water Pool of water

Adding pressure to gas under a piston Before 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. Each 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 P = F/A + P0 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.