Joule's Experiment and the First Law of Thermodynamics

heating time T (s)

55

electromotive force E (V)

1

resistor R (Ω)

0.01

initial temperature

t

0

(°C)

20.

water depth h (cm)

10

inside diameter

r

1

(cm)

15

agitator radius

r

2

(cm)

9

Joule's experiment demonstrated the validity of the first law of thermodynamics. Electrical or mechanical energy can be converted into thermal energy, but the total amount of energy is conserved. In this Demonstration, the amount of heat

Q

in joules generated in a circuit element of resistance

R

(immersion heater) is measured by a calorimeter. Assume that all the heat is absorbed by the water and measure the temperature increase from

t

0

to

t

. Then

Q=mcΔt=ρπ

2

r

1

h

-6

10

c(t-

t

0

)

.

Joule's law gives

Q

liberated by current

I

flowing through a resistor with resistance

R

for a time

T

,

Q=

2

I

RT

.

Using Ohm's Law

I=E/R

, we obtain

2

I

RT=

2

E

T/R

; therefore

ρπ

2

r

1

h

-6

10

c(t-

t

0

)=

2

E

T/R

,

t=

2

E

T

ρπ

2

r

1

h

-6

10

cR

+

t

0

.

The final temperature

t

(in ºC) and the energy gained by the water

Q

(in J) are shown on the diagram.