By Colin Slade

By Colin Slade

alphabet soup

alphabet soup

the known stuff

the known stuff

Lighter D = .02 m t = .001 m T = 50 ºC kNichrome = 11.3

W/m-K cp Nichrome = 450

J/kg-K Nichrome = 8400

kg/m3

Lighter D = .02 m t = .001 m T = 50 ºC kNichrome = 11.3

W/m-K cp Nichrome = 450

J/kg-K Nichrome = 8400

kg/m3

Steel Can

D = .066

m t = .001

m T = 20 ºC

kSteel = 40

W/m-K

Steel Can

D = .066

m t = .001

m T = 20 ºC

kSteel = 40

W/m-K

Alphabet Soup

D = .064 m

H = .093 m

m = .305 kg

ksoup = .643

W/m-K

cp soup = 4186

J/kg-K

soup = 997

kg/m3

Tdone = 40 ºC

Alphabet Soup

D = .064 m

H = .093 m

m = .305 kg

ksoup = .643

W/m-K

cp soup = 4186

J/kg-K

soup = 997

kg/m3

Tdone = 40 ºC

assumptionsassumptions

The can is inside

the car and assume

d to be

at the same temper

ature as the quies

cent

air. Convection, f

orced and free, ca

n be

neglected.

The can does not r

each a sufficientl

y high

temperature and ra

diation can be neg

lected

as well.

Therefore, heat tr

ansfer is due only

to

conduction from th

e lighter to the c

an.

The can is inside

the car and assume

d to be

at the same temper

ature as the quies

cent

air. Convection, f

orced and free, ca

n be

neglected.

The can does not r

each a sufficientl

y high

temperature and ra

diation can be neg

lected

as well.

Therefore, heat tr

ansfer is due only

to

conduction from th

e lighter to the c

an.

calculations

calculations

Heat provided by t

he

lighter

qconduction = mcp Nichrom

eT

T = Tlighter - Tcan

= 30 C

m = V = At = .00

3 kg

qconduction = 35

.6 W

Heat provided by t

he

lighter

qconduction = mcp Nichrom

eT

T = Tlighter - Tcan

= 30 C

m = V = At = .00

3 kg

qconduction = 35

.6 W

Resistances of the Can and the SoupRcan = t/ksteelA = .007 W/KRsoup = H/ksoupA = 45 W/KRtotal = Rcan + Rsoup =

45.007 W/K

Resistances of the Can and the SoupRcan = t/ksteelA = .007 W/KRsoup = H/ksoupA = 45 W/KRtotal = Rcan + Rsoup =

45.007 W/K

Time required to cook the alphabet soupModified Lumped

Capacitance using Rtotalt = cp V Rtotal ln(Tlighter - Tcan / Tlighter - Tdone)

V = m = .305 kgt = 63128 s = 1052 mins = 17 hours

Time required to cook the alphabet soupModified Lumped

Capacitance using Rtotalt = cp V Rtotal ln(Tlighter - Tcan / Tlighter - Tdone)

V = m = .305 kgt = 63128 s = 1052 mins = 17 hours

conclusionsconclusions

There is no way you could cook a can of soup with a single car lighter. It simply does not produce enough heat.

There is no way you could cook a can of soup with a single car lighter. It simply does not produce enough heat.