PHY 231 1 PHYSICS 231 Lecture 25: Heat & Heat exchange Remco Zegers Walk-in hour:Tue 4-5 pm...
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Transcript of PHY 231 1 PHYSICS 231 Lecture 25: Heat & Heat exchange Remco Zegers Walk-in hour:Tue 4-5 pm...
PHY 2312
Boyle & Charles & Gay-LussacIDEAL GAS LAW
PV/T = nR
n: number of particles in the gas (mol)R: universal gas constant 8.31 J/mol·K
If no molecules are extracted from or added to a system:
2
22
1
11 constant T
VP
T
VP
T
PV
PHY 2313
M
RT
m
Tkvv
nRTTNkE
Tkvm
vmk
T
TNkPV
vmNPV
brms
Bkin
B
B
B
33
2
3
2
32
3
2
1
)2
1(
3
2
2
1
3
2
2
2
2
2
Microscopic
Macroscopic
Temperature ~ average molecular kinetic energy
Average molecular kinetic energy
Total kinetic energy
rms speed of a moleculeM=Molar mass (kg/mol)
PHY 2314
Internal energyIn chapter 10: The internal (total) energy for an idealgas is the total kinetic energy of the atoms/particlesin a gas.
For a non-ideal gas: the internal energy is due to kineticand potential energy associated with:• translational motion• rotational motion• vibrational motion• intermolecular potential energy
|PEideal gas=0| < |PEnon-ideal gas| < |PEliquid| < |PEsolid|
PE
RPE: negative!
PHY 2315
Heat
Heat: The transfer of energy between objectsbecause their temperatures are different.
Heat: energy transfer Symbol: Q
Units: Calorie (cal) or Joule (J) 1 cal = 4.186 J (energy needed to raise
1g of water by 10C)
PHY 2316
Heat transfer to an object
Q=cmT
Energy transfer(J or cal)
Specific heat(J/(kgoC) or cal/(goC)
Mass of object
Change in temperature
The amount of energy transfer Q to an object with mass m when its temperature is raised by T:
PHY 2317
Example
A 1 kg block of Copper israised in temperature by10oC. What was the heattransfer Q.?
PHY 2318
Another one
A block of Copper is dropped from a height of10 m. Assuming that all the potential energy is transferredinto internal energy (heat) when it hits the ground, what is the raise in temperature of the block (ccopper=387 J/(kgoC))?
PHY 2319
Calorimetry
If we connect two objects with different temperatureenergy will transferred from the hotter to the coolerone until their temperatures are the same. If the system is isolated:
Qcold=-Qhot
mcoldccold(Tfinal-Tcold)=-mhotchot(Tfinal-Thot)
the final temperature is: Tfinal=
mcoldccoldTcold+mhotchotThot
mcoldccold+mhotchot
PHY 23110
question
A block of iron that has been heated to 1000C is droppedin a glass of water at room temperature (200C). After the temperature in the block and the water has become equal:
a) The water has changed more in temperature than the iron block.b) The water has changed less in temperature than the iron blockc) the temperatures of both have changed equallyd) it is not possible to answer this.
PHY 23111
An exampleThe contents of a can of soda (0.33 kg) which is cooled to 4oC is poured into a glass (0.1 kg) that is atroom temperature (200C). What will the temperatureof the filled glass be after it has reached full equilibrium(glass and liquid have the same temperature)?Given cwater=4186 J/(kgoC) and cglass=837 J/(kg0C)
PHY 23112
And another
A block of unknown substance with a mass of 8 kg, initiallyat T=280K is thermally connect to a block of copper (5 kg)that is at T=320 K (ccopper=0.093 cal/g0C). After the system has reached thermal equilibrium the temperature T equals 290K. What is the specific heat of the unknown materialin cal/goC?
????
copper
PHY 23113
Demo: heating water with a ball of Lead
A ball of Lead at T=100oC with mass 300 g is dropped in aglass of water (0.3 L) at T=200C. What is the final (after thermal equilibrium has occurred) temperature ofthe system? (cwater=1 cal/goC, clead=0.03 cal/goC water=103kg/m3)
PHY 23114
Phase Change
GAS(high T)
liquid (medium T)
Solid (low T)Q=cgasmT
Q=cliquidmT
Q=csolidmT
Gas liquid
liquid solid
PHY 23115
Phase changeGas liquid
When heat is added to a liquid, potential energy goes to 0 (the energy stored in the stickiness of the liquid is taken away) DURING THE CHANGE FROM LIQUID TO GAS, THE KINETIC
ENERGY DOES NOT CHANGE AND SO THE TEMPERATUREDOES NOT CHANGE.
ALL ADDED HEAT GOES TO CHANGING PE
When heat is taken from a gas, potential energy goes to the stickiness of the fluid
DURING THE CHANGE FROM GAS TO LIQUID, THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE
DOES NOT CHANGE.ALL REMOVED HEAT GOES TO CHANGING PE
PHY 23116
Phase change liquid solid
When heat is added to a solid to make a liquid, potential energy in the bonds between the atoms become less
DURING THE CHANGE FROM SOLID TO LIQUID, THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE
DOES NOT CHANGE.ALL ADDED HEAT GOES TO CHANGING PE
When heat is taken from a liquid, the bonds between atoms becomes stronger (potential energy is more negative)
DURING THE CHANGE FROM LIQUID TO SOLID, THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE
DOES NOT CHANGE.ALL REMOVED HEAT GOES TO CHANGING PE
PHY 23117
Okay, the Temperature does not change in a phase transition!
But what is the amount of heat added to make the phase transition?
Gas liquid
Qgasliquid=-MLv
Qliquidgas=+MLv
Lv=latent heat of vaporization (J/kg or cal/g)depends on material.
Use the table 11.2 in the book for LON-CAPA
M:mass
PHY 23118
solid liquid
Qliquidsolid=-MLf
Qsolidliquid=+MLf
Lf=latent heat of fusion (J/kg or cal/g)depends on material.
M:mass
Use the table 11.2 in the book for LON-CAPA
PHY 23119
Phase Change
GAS(high T)
liquid (medium T)
Solid (low T)Q=cgasmT
Q=cliquidmT
Q=csolidmT
Gas liquid
liquid solid
Q=mLf
Q=mLv
PHY 23121
Ice with T=-30oC is heatedto steam of T=1500C.How many heat (in cal) hasbeen added in total?cice=0.5 cal/goCcwater=1.0 cal/goCcsteam=0.480 cal/goCLf=540 cal/gLv=79.7 cal/gm=1 kg=1000gA) Ice from -30 to 0oC Q=1000*0.5*30= 15000 cal
B) Ice to water Q=1000*540= 540000 calC) water from 0oC to 100oC Q=1000*1.0*100=100000 calD) water to steam Q=1000*79.7= 79700 calE) steam from 100oC to 1500C Q=1000*0.48*50=24000 cal TOTAL Q= =758700 cal