Eunil Won Dept. of Physics, Korea Univ 1

Ch 05 Temperature and Heat

Eunil Won Dept. of Physics, Korea Univ 2

TemperatureWhat is temperature?

: is a quantitative measure of hot and cold

(as physicists, we need more precise definition of the temperature but for now let’s take the above statement)

From the experience, we know that

boiling point of water : 100 oCtemperature of the universe : 3 K

Temperature is directly related to the kinetic energy of the molecules

SI unit: Kelvin (K) Ex) 0 K = -273.15 oC

Eunil Won Dept. of Physics, Korea Univ 3

Thermal ExpansionMost materials expand when their temperature is increased

α: coefficient of linear expansion

Material α (1/oC)

Aluminum 25 x 10-6

Lead 29 x 10-6

Glass 9 x 10-6

Quartz 0.4 x 10-6

Gasoline 320 x 10-6

Water 70 x 10-6

Air 1100 x 10-6

This is the operational principle of most of thermometers

Eunil Won Dept. of Physics, Korea Univ 4

Water has highest density at 4 oC

Specific heat?

Eunil Won Dept. of Physics, Korea Univ 5

Example 5.1

cm 105.4C)cm)(3.0C)(3.0/10(60

4

6

−

−

×=

°°×=∆=∆ TLL α

What is the change in length of a column of mercury 3.0 cm long if its temperature increases from 37℃ to 40℃?

Eunil Won Dept. of Physics, Korea Univ 6

Example 5.2

kg 1.05g 101.05)cm )(10g/cm (1.05

3

333

=×=

== Vm ρ

What is the mass of a liter of whole blood?

]kg/m[ 3⇒=Vmρdensity

Eunil Won Dept. of Physics, Korea Univ 7

Specific Heat

)()( fifi TTCTTQ −=−∝

dTdQ

nCs 1

mol=≡

]KJ/kg4190Ccal/g1[ ⋅=⋅ο

dTdQC ≡

TsmQ ∆=

Eunil Won Dept. of Physics, Korea Univ 8

Example 5.3

kcal 1cal 1000C) g)(5.0 C)(200cal/g (1.00

www

==°°⋅=

∆= TmsQ

cal 03C) g)(5.0 C)(200cal/g (0.030

PbPbPb

=°°⋅=

∆= TmsQ

(a) Heat to increase the temperature of 200 g of water 5.0oC?

(a) Heat to increase the temperature of 200 g of lead 5.0oC?

Eunil Won Dept. of Physics, Korea Univ 9

Example 5.4

mghTsmQ

2121 PE

=∆=

C 0.78

CJ

/smkg0.78

J) C)(4186kcal/kg 2(0.030m) )(20m/s (9.8

2

22

2

°=

°⋅=

°⋅=

=∆s

ghT

Calculate the temperature increase of a lead ball dropped from a height of 20 m, assuming that half the thermal energy generated on impact goes into the ball

Eunil Won Dept. of Physics, Korea Univ 10

Phase changes and latent heat

fmhQ = vmhQ =

Gas state

Solid state

Liquid state

Latent heat: heat needed to make phase change

(boiling water)

m: mass of object

Phase change: changes of a substance from one phase of matter to another

hf: heat of fusion hv: heat of vaporization

Eunil Won Dept. of Physics, Korea Univ 11

Example 5.5

cal 106.40cal/g) g)(80 (800

4

f

×=== mhQ

11minhr,1

s 104.27cal/s15

cal 106.40/

34

=

×=×=

=tQ

Qt

An aluminum ice cube tray contains 800 g of water at 0oC. If heat is removed at the rate of 15 cal/sec, how long will it take for all of the water to freeze?

From table 5.4

Eunil Won Dept. of Physics, Korea Univ 12

Example 5.7

g 93.8cal/g 80

cal 7500

f

iiww

wwfii

fiicold

wwhot

hotcold

==∆−∆=∴

∆=+∆+∆=∆

∆=∆∆=∆

hTmsTmsm

TmsmhTmsmhTmsQ

TmsQQQ

Suppose that 100 g of ice at an initial temperature of -10oC are put into 400 g of water at an initial temperature of 20oC. How many grams of ice melt? (For simplicity, ignore the effects of the container)

Eunil Won Dept. of Physics, Korea Univ 13

Evaporation

Random motion of molecules

Small fraction of them has high kinetic energy escape from substance

relative humidity=vapor density/saturation vapor density

Saturation vapor density: maximum amount of vapor density that air can hold at a given temperature

Eunil Won Dept. of Physics, Korea Univ 14

Example 5.6

g 427cal/g 204

C) g)(1.5 10C)(70cal/g (0.83 3v

ppalc

ppvalc

palc

=°×°⋅=

∆=

∆=

=

hTms

m

Tmshm

QQ

One method of reducing a high body temperature very quickly is to give a patient an alcohol rub. How many grams of alcohol must be evaporated from the surface of 70 kg person to reduce his temperature by 1.5oC?

From table 5.3

From table 5.4

Eunil Won Dept. of Physics, Korea Univ 15

Conduction : contact between substances

Rate of heat transfer between two substances in contact: d

TTkAtQ CH −=

k: coefficient of thermal conductivity

d

THTC

Area A

Eunil Won Dept. of Physics, Korea Univ 16

Thermal conductivities of common substances

Thermal Conductivity (J/sec m oC)Silver 420Copper 380Aluminum 200Steel 40Ice 2.0Glass (average) 0.84Concrete, brick 0.84Human tissue without blood 0.2Wood 0.08-0.16Air 0.023

Eunil Won Dept. of Physics, Korea Univ 17

Example 5.8

W120J/s 120m 0.01

C)33C)(37m C)(1.5mJ/s (0.2

)(

2

21

==

°−°°⋅⋅=

−=d

TTkAtQ

Calculate the rate of heat conduction out of a human body, making the following assumptions: the interior temperature is 37oC, skin temperature is 33oC, the area of the person is 1.5 m2, and the thickness of the tissues averages 1.0 cm.

Eunil Won Dept. of Physics, Korea Univ 18

Convection : movement of molecules

Eunil Won Dept. of Physics, Korea Univ 19

Radiation : Electromagnetic wave

4eATPtQ σ==

)TT(eA

PPP42

41

emitabsnet

−σ=

−=

The amount of heat radiated per unit time:

σ: 5.67x10-8 J/sec m2K4

A: area of the objecte: emissivity

Eunil Won Dept. of Physics, Korea Univ 20

Example 5.9

115W]93K)2)[(306Km 5)(0.97)(1.KmJ/s 10(5.67

)(/44248

42

41

=⋅⋅×=

−=

-()

TTeAtQ-

σ

What is the heat transfer by radiation from an unclothed person standing in a dark room of temperature 20oC? The person’s skin temperature is 33oC, and the exposed area of his skin is 1.5 m2.

Note: assume the emissivity is 0.97 for human skin

Eunil Won Dept. of Physics, Korea Univ 21

Heat and the Human Body

What are the body’s mechanisms for getting rid of excess heat?

Circulation of blood

Evaporation of perspiration from the skin

Evaporation of water from the lungs

Eunil Won Dept. of Physics, Korea Univ 22

Example 5.10

inout

in

PPEffP

/W400

==

W32080WW400)2.0(

=−===

outinheat

out

PPPP

cal4587)J186.4/cal1)(s60)(s/J320(tPQt/QP heatheat ===⇒=

7.9g/gcal/580cal4587/ ===⇒= vv hQmmhQ

On a day when air temperature is 34oC (normal skin temperature) a cyclist is maintaining a speed of 15 km/hr. How many grams of water must this cyclist evaporate per minute?

Note: power consumption of cycling is 400 W with efficiency 20% (80% goes to heat)

heat of evaporation of water : 580 cal/gm

Eunil Won Dept. of Physics, Korea Univ 23

Example 5.11

C4.4g)10C)(763cal/g0min)/(0.8cal/min)(64587(

sm/QTTsmQ3o

°=×=

=∆⇒∆=

How much will the temperature of the cyclist in Ex. 5.10 increase in one hour if none of the body heat generated is lost to the surroundings? Assume the cyclist’s mass is 76 kg and specific heat is 0.83 cal/goC

Eunil Won Dept. of Physics, Korea Univ 24

Example 5.12

kW 6.3 W6300

person) (30 W/person)(210heat

===P

kcal 105.4cal105.4

min)person)(50 person](30/min)(kcal/0.3[

3

6

×=×=

=Q

(a) Calculate the power in waste heat put into a classroom by 30 students. (b) How many calories of energy do the students put into the room during a 50-min lecture?

Note: energy consumption rate by sitting in class=210W(or 3.0 kcal/min)

Eunil Won Dept. of Physics, Korea Univ 25

Heat: Diagnostic and Therapeutic uses

Example:

Thermography