1. PHYSICS 231 Lecture 28: Conduction,Convection & Radiation
Remco Zegers
walk-in: Monday 9:15-10:15
Helproom
PHY 231

2. Heat transfer to an object
The amount of energy transfer Q to an object with mass m
when its temperature is raised by T:
Q=cmT
Change in
temperature
Mass of object
Energy transfer
(J or cal)
Specific heat
(J/(kgoC) or cal/(goC)
PHY 231

3. Phase Change GAS(high T) Q=cgasmT Q=csolidmT Solid (low T) liquid 
Q=mLv
liquid (medium T)
Q=mLf
Q=cliquidmT
PHY 231

4. quiz (extra credit) A block of gold (room temperature 200C)
is found to just melt completely after
supplying 4x103 J of heat. What
was the mass of the gold block?
Given: Lf=6.44x104 J/kg Tmelt=1063oC cspecific=129 J/kg0C
0.01 kg
0.02 kg
0.03 kg
0.06 kg
10 kg
Q=cmT+mLf
=129*m*1043+m*6.44x104
=2x105*m
4000=2x105m
m=0.02 kg
PHY 231

5. How can heat be transferred?
PHY 231

6. Conduction Touching different materials: Some feel cold, others
feel warm, but all are at the same temperature…
PHY 231

7. Thermal conductivity metal T=200C wood T=200C The heat transfer
in the metal is
much faster than
in the wood:
(thermal
conductivity)
T=370C
T=370C
PHY 231

8. Heat transfer via conduction
Conduction occurs if there is a
temperature difference between
two parts of a conducting medium
Rate of energy transfer P
P=Q/t (unit Watt)
P=kA(Th-Tc)/x=kAT/x
k: thermal conductivity
Unit:J/(msoC)
metal k~300 J/(msoC)
gases k~0.1 J/(msoC)
nonmetals~1 J/(msoC)
PHY 231

9. Example A glass window (A=4m2,x=0.5cm)
separates a living room (T=200C)
from the outside (T=0oC). A) What
is the rate of heat transfer through
the window (kglass=0.84 J/(msoC))?
B) By what fraction does it change
if the surface becomes 2x smaller
and the temperature drops to -200C?
A) P=kAT/x=0.84*4*20/0.005=13440 Watt
B) Porig=kAT/x Pnew=k(0.5A)(2T)/x=Porig
The heat transfer is the same
PHY 231

10. Another one. Heat sink Heat reservoir
An insulated gold wire (I.e. no heat lost to the air) is at
one end connected to a heat reservoir (T=1000C) and at the
other end connected to a heat sink (T=200C). If its length
is 1m and P=200W what is its cross section (A)?
kgold=314 J/(ms0C).
P=kAT/x=314*A*80/1=25120*A=200
A=8.0E-03 m2
PHY 231

11. And another Water 0.5L 1000C A=0.03m2 thickness: 0.5cm. 1500C
A student working for his exam feels hungry and starts boiling
water (0.5L) for some noodles. He leaves the kitchen when
the water just boils.The stove’s temperature is 1500C.
The pan’s bottom has dimensions given above. Working hard
on the exam, he only comes back after half an hour. Is there
still water in the pan? (Lv=540 cal/g, kpan=1 cal/(ms0C)
To boil away 0.5L (=500g) of water: Q=Lv*500= cal
Heat added by the stove: P=kAT/x=1*0.03*50/0.005=
=300 cal
P=Q/t t=Q/P=270000/300=900 s (15 minutes)
He’ll be hungry for a bit longer…
PHY 231

12. Isolation Tc Th inside L1 L2 L3
A house is built with 10cm thick wooden walls and roofs.
The owner decides to install insulation. After installation
the walls and roof are 4cm wood+2cm isolation+4cm wood.
If kwood=0.10 J/(ms0C) and kisolation=0.02 J/(ms0C), by what
factor does he reduce his heating bill?
Pbefore=AT/[0.10/0.10]=AT
Pafter=AT/[0.04/ / /0.10]=0.55AT
Almost a factor of 2 (1.81)!
PHY 231

13. Convection
T high
 low
PHY 231

14. Radiation Nearly all objects emit energy through radiation:
P=AeT4 : Stefan’s law (J/s)
=5.6696x10-8 W/m2K4
A: surface area
e: object dependent constant emissivity (0-1)
T: temperature (K)
P: energy radiated per second.
PHY 231

15. emissivity Ideal absorber (black body) Ideal reflector e=1 e=0
all energy is absorbed
also ideal radiator!
Ideal reflector
e=0
no energy is absorbed
PHY 231

16. A BBQ
The coals in a BBQ cover an area of 0.25m2. If the emissivity of the burning coal is 0.95 and their temperature 5000C, how much energy is radiated every
minute?
P=AeT4 J/s
=5.67x10-8*0.25*0.95*(773)4=4808 J/s
1 minute: 2.9x105 J (to cook 1 L of water 3.3x105 J)
PHY 231

17. radiation balance
If an object would only emit radiation it would eventually
have 0 K temperature. In reality, an object emits AND
receives radiation.
P=Ae(T4-T04) where
T: temperature of object
T0: temperature of surroundings.
PHY 231

18. example The temperature of the human body is 370C. If the
room temperature is 200C, how much heat is given
off by the human body to the room in one minute?
Assume that the emissivity of the human body is 0.9
and the surface area is 2 m2.
P=Ae(T4-T04)
=5.67x10-8 * 2 * 0.9 *( )=
=185 J/s
Q=P*T=185*60=1.1x104 J
PHY 231