PHY 2311

PHYSICS 231Lecture 25: Heat & Heat exchange

Remco ZegersWalk-in hour:Tue 4-5 pm

Helproom

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 23120

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