HEAT

Thermal energy –The kinetic and potential energy of the random microscopic motion of molecules, atoms, ions, electrons & other particles Heat –The thermal energy transferred from a hotter body to a colder body.

calorie (cal) –Unit of heat –The amount of heat needed to raise the temperature of 1 gram of water 1⁰ C 1 kcal = 1000 cal = 1 (food) Calorie British Thermal Unit (BTU) –The thermal energy transferred from a hotter body to a colder body 1 BTU = 0.252kcal.

Q = mcΔT

example You mix 1.0kg water at 80⁰C with 1.0 kg water at 20⁰C. What is the final temperature Q = mcΔT Q 80⁰C = Q 20⁰C (mcΔT) 80⁰C = (mcΔT) 20⁰C (1.0kg)(4187J/kg· ⁰C)(80-T) = (1.0kg)(4187J/kg· ⁰C)(T-20) – 4187 T = 4187 T – T = T = 50 ⁰C

Mechanical equivalent of heat –The conversion factor between calories and joules 1 cal = 4.187J –You need to convert thermal energy in calories to joules to relate to kinetic energy ( 1/2 mv 2 ) or potential energy (mgy).

Thermal expansion –Expanding solids maintain original shape –Expanding liquids conform to the container Linear expansion ΔL = αLΔTL = length α = coefficient of liner expansion ΔT = temperature change

Example: The highest tower in the world is the steel radio mast of Warsaw Radio in Poland, which has a height if 646m. How much does its height increase between a cold winter day when the temperature is -35⁰C and a hot summer day when the temperature is +35 ⁰C ? ΔL = αLΔT = 12x10 -6 / ⁰C x 646 x 70 ⁰C = 0.54m

Volume expansion ΔV= βVΔTL = length β = coefficient of liner expansion ΔT = temperature change coldhot Β = 3 α

convection –Heat is stored in a moving fluid and is carried from one place to another by the motion of this fluid radiation ΔL = αLΔTL = length α = coefficient of liner expansion ΔT = temperature change

radiation –The heat is carried from one place to another by electromagnetic waves RADIATION

Specific Heat of a Gas Molar Specific Heat at a constant volume the heat absorbed during the change of state Q = nC v ΔT Q = amount of heat required n = number of moles C v = specific heat at a constant volume ΔT = Change in temperature Molar Specific Heat at a constant pressure the heat absorbed during the change of state Q = nC p ΔT C p = specific heat at a constant pressure

Q = nC v ΔT with a small amount of heat, the energy must match dQ = dE so nC v ΔT = dE The force of the gas on the piston is pA and the work done by the gas is dW = Fdx so dW = pA dx Adx is the small change dV of volume dW = pdV dQ = dE+ dW = dE + pdV or nC p dT = dE +pdV nC p dT = nC V dT + pdV Ideal gas Law pdV = nRdT nC p dT = nC V dT + nRdTC p = C V + R R = 8.31 J/K·mol or 1.99 cal/K·mol