PHYS1003 LECTURE 3 HEAT AND INTERNAL ENERGY Outline 1 Microscopic description of an ideal gas 2 Heat and internal energy 3 Heat Capacity 4 Phase change of matters 1 REVIEW IDEAL GAS What we can learn from gas thermometers GAY LUSSAC LAW p T constant at a fixed V p1 T1 p2 T2 p1 T1 p2 T2 BOYLE MARRIOT LAW pV constant at a fixed temperature IDEAL GAS LAW pV nRT NkBT CHEMIST PHYSICIST n number of particles mole R gas constant R 8 314 J mol 1K 1 N particle number kB Boltzman s constant kB 1 381 10 23J K 1 IDEAL GAS LAW describes energy of the gas 2 IDEAL GAS What we can learn from gas thermometers IDEAL GAS LAW pV nRT NkBT CHEMIST PHYSICIST n number of particles mole R gas constant R 8 314 J mol 1K 1 N particle number kB Boltzman s constant kB 1 381 10 23J K 1 IDEAL GAS LAW describes energy of the gas 3 IDEAL GAS Real Gas vs Ideal Gas OBSERVATION All real gases have the same value of pV nT when P 0 IDEAL GAS An ideal gas is defined as a gas of point like gas particles with negligible inter particle forces 4 KINETIC GAS THEORY MICROSCOPIC PICTURE OF MACROSCOPIC FUNCTIONS MACROSCOPIC GAS PROPERTIES p V T Can be explained in terms of ensemble averages of kinetic energy of ideal gas particles KEY IDEA Elastic collisions of gas particles with reservoir wall of area A exert pressure p 2 2 2 1 2 vx 2 ensemble average average over all molecules A MOLECULAR PICTURE OF TEMPERATURE 2 using gas equation pV NkBT 2 2 2 2 3 1 2 2 1 2 2 1 2 3 2 IDEAL GAS Temperature Kinetic Energy Ekin 5 PRESSURE ON A WALL PROOF Momentum change on a mass when it bounce back once 2 On average a mass bounces once on one wall in time to travel back and fro 2 Force acting on the mass p 2 2 Amount of force acting on the wall Amount of force acting on the mass Newton s 3rd Law 2 Average force acting on the wall Pressure 2 2 3 2 2 for one mass 6 DEMO Kinetic Theory Model https youtu be my ossbm4S0 7 Internal Energy of a Real Gas It s not just about moving fast INTERNAL ENERGY U Kinetic Energy Potential Energy of all the molecules in the system Potential energy due to the interactions among the molecules in the system attraction repulsion The more ways the molecule moves the more ways the system can acquire KE Similarly the more interactions among the molecules the more the system can acquire PE 8 EXAMPLES OF INTERNAL ENERGY IN GAS Degree of freedom DOF kinds of kinetic or rotational energy Monoatomic gas Diatomic gas Rotation end over end about the z axis Rotation end over end about the y axis DOF 3 Translations Rotation about its own axis DOF 3 Translations 2 Rotations 9 EQUIPARTITION THEOREM the same amount of energy of 1 2 In thermal equilibrium for each molecule each kind of kinetic and rotational energy carries For ideal gas internal energy U Number of molecule j Monatomic gas Diatomic gas When temperature increases the internal energy increases for gases 1 2 Translational Rotational Potential energy from intermolecular interaction usually negative as they are attractive 10 Thermodynamic Phase Transitions what happens when temperature increases Thermodynamic Phase Transitions What happens when temperature increases U Temperature T 12 Less interaction Less PE contribution Higher internal energy No PE only KE in the internal energy U Thermodynamic Phase Transitions What happens when temperature increases EXAMPLE Water 13 DEMO Banana Hammer https youtu be FOdujjnr0kk 14 Why we cannot live on mars yet No liquid water on mars surface or not p 760 mm Hg T 15 C EXAMPLE Water Pressure on Mars is too low to sustain liquid water p 4 77 mm Hg T 63 C Why pressure is so low 15 Heating Up Materials Requires Energy Q Specific Heat heat capacity SPECIFIC HEAT c m mass c kJ kg 1 K 1 SPECIFIC HEAT is a material dependent property SPECIFIC HEAT reflects the different composition of internal energy When a system absorbs heat Energy distributed to different components KE or PE of the internal energy Temperature increases Different composition of internal energy in different matters Energy required to rise 1 C or 1 K is different Different Specific Heat how difficult to heat up something 16 EXAMPLE HEAT CAPACITY IN GAS ENERGY REQUIRED TO INCREASE 1 C PER MOLE More components in internal energy Each DOF takes less share of the input energy More total heat is needed to increate Temp by 1 K 17 Heating Up Materials Requires Energy Q Specific Heat heat capacity SPECIFIC HEAT c m mass c kJ kg 1 K 1 SPECIFIC HEAT of water cw cW 4 184 kJ kg 1 K 1 1 kcal kg 1 K 1 1 kcal energy to heat up m 1kg of water by T 1 K EXAMPLE Heating of 1 kg H20 from ice using 4 kW 18 Phase Transitions Require Energy Q Latent Heat happens at a fixed T LATENT HEAT LS m mass LS kJ kg 1 Latent heat of Value boiling water 100 o melting ice 0 C o 3 C 2 257 10 kJ kg 1 2 kJ kg 3 33 10 1 EXAMPLE Heating of 1kg H20 using 4 kW 19 PHASE TRANSITIONS REQUIRE ENERGY Q LATENT HEAT Changes in temperature and phase are accompanied by a change in internal energy EXAMPLE Heating of 1kg H20 using 4 kW 20 QOD QUESTION OF THE DAY AN EXAMPLE How much energy density is in coal in MJ kg Thought Chemical energy is released from the carbon bonds in the coal For 1 kg of coal we need to know how many carbon are there and for each kg of carbon how much energy is released Data we need Energy release by carbon combustion 178 kcal 24 g How many carbon is in 1kg of coal 75 Converting the number into MJ kg 21 QOD QUESTION OF THE DAY AN EXAMPLE How much energy density is in coal Energy release by carbon combustion 178 kcal 24 g How many carbon is in coal 75 60 90 Converting the number into MJ kg 22 QOD QUESTION OF THE DAY AN EXAMPLE How much energy density is in coal Energy release by carbon combustion 178 kcal 24 g How many carbon is in coal 75 60 90 Converting the number into MJ kg 1kg of coal 750g Carbon 178kcal 24g 750g 5562 kcal 23 271kJ 23MJ Fuel Coal Crude oil Gasoline Natural Gas MJ kg 20 26 41 42 44 45 53 54 Ans 20 26 MJ kg Source V Smil 2006 Energy 23 QOD QUESTION OF THE DAY MAKING SENSE OF THE NUMBERS Town Gas claims their gas has an energy density Calorific Value of 17 3 MJ m3 by volume Eqv 0 52x1 2 kg m3 0 6 kg m3 How much energy density is released from methane combustion in Towngas in …