2. HE WAS A FRENCH PHYSICIST AND BALLOONIST
WHO OBSERVED THE RELATIONSHIP BETWEEN THE
VOLUME AND THE ABSOLUTE TEMPERATURE OF AN
IDEAL GAS HELD AT CONSTANT PRESSURE . HE
WAS BORN ON 12TH OF NOVEMBER 1746 AND DIED
ON 7TH OF APRIL 1823. CHARLES WROTE ALMOST
NOTHING ABOUT MATHEMATICS, AND MOST OF
WHAT HAS BEEN CREDITED TO HIM WAS DUE TO
MISTAKING HIM WITH ANOTHER JACQUES
CHARLES, ALSO A MEMBER OF THE PARIS
ACADEMY OF SCIENCES, ENTERING ON 12 MAY
1785. HE WAS SOMETIMES CALLED CHARLES THE
GEOMETER.
3. IN HIS EXPERIMENT, CHARLES UTILIZED A
SIMILAR APPARATUS TO BOYLE’S. HE
TRAPPED A PARTICULAR AMOUNT OF GAS IN
THE SHORT SEALED END OF A J-SHAPED
TUBE, USING MERCURY, AND IMMERSED IT IN
A HEATED WATER BATH. WHILE KEEPING THE
PRESSURE CONSTANT, CHARLES ADJUSTED
THE TEMPERATURE OF THE WATER
GRADUALLY AND OBSERVED HOW THE
VOLUME OF THE TRAPPED GAS CHANGED. HE
NOTICED THAT AS THE TEMPERATURE OF THE
WATER ROSE, THE VOLUME OF THE GAS
INCREASED. THUS, CHARLES’ LAW
EXPLAINED THAT AT CONSTANT PRESSURE,
THE VOLUME OF A FIXED AMOUNT OF GAS IS
DIRECTLY PROPORTIONAL TO ITS ABSOLUTE
TEMPERATURE.
4. THE RELATIONSHIP OF THE VOLUME
AND THE ABSOLUTE TEMPERATURE OF
GAS AT CONSTANT PRESSURE IS GIVEN
BY THE EQUATION V = kT, WHICH IS
DERIVED FROM THE FOLLOWING:
V ∝ T
V = kT or
V
T
= k
where V = VOLUME
T = TEMPERATURE
K = A CONSTANT VALUE
5. FIGURE
11.6
(a) AT CONSTANT PRESSURE, THE
VOLUME OF THE GAS AT 400 K IS 35 L; (b)
AS THE TEMPERATURE IS DOUBLED TO
800 K , THE VOLUME ALSO DOUBLES TO
70 L.
V
T
= k
V
T
= k
k = 35 L
400 K
k = 70 L
800 K
k =
K
0.0875 L
k =
0.0875 L
K
6. SINCE k IS CONSTANT, INCREASING THE
TEMPERATURE AND VOLUME SHOULD RESULT
IN THE SAME VALUE. IT CAN BE INFERRED FROM
THE EQUATION OF CHARLES’ LAW THAT THE
INITIAL AND FINAL AMOUNTS OF THE VOLUME
AND THE ABSOLUTE TEMPERATURE ARE EQUAL.
THUS, IN MATHEMATICAL FORM, THIS IS
EXPRESSED AS:
V
i
T
i
=
V
f
T
f
O
R
Vi Tf = Vf
Ti
wher
e
Vi = INITIAL VOLUME
Ti = INITIAL TEMPERATURE
Vf = FINAL VOLUME
Tf = FINAL TEMPERATURE
7. EXAMPLE 1
A 5 L SAMPLE OF ARGON (Ar), A NOBLE GAS, HAS BEEN TRAPPED INSIDE A
GLASS TUBE THAT IS IMMERSED IN A WATER BATH HEATED AT 340 K.
ASSUMING THAT THE PRESSURE IS HELD CONSTANT, HOW DOES THE
VOLUME CHANGE IF THE TEMPERATURE OF THE WATER BATH IS INCREASED
TO 550 K?
GIVEN V1 = 5 L
T1 = 340 K
T2 = 550 K
FIND V2 = ?
9. EXAMPLE 2
A HOT AIR BALLOON FLOWN DURING THE FESTIVAL IN PAMPANGA CONTAINED
12 m3 OF AIR HEATED INITIALLY AT 220 C. AS THE BALLOON FLOATED, THE
VOLUME OF AIR LIFTING THE BALLOON ROSE TO 17 m3 AT CONSTANT
ATMOSPHERIC PRESSURE. WHAT WAS THE FINAL TEMPERATURE OF THE AIR?
GIVEN V1 = 12 m3
T1 = 220 C
V2 = 17 m3
FIND T2 = ?
