Thursday, May 26, 2011

Charle’s Law


The relationship between temperature of a gas and its volume was studied by Jacques Charles in 1787 and was further modified by Gay-Lussac in 1802. They gave a generalization known as Charle’s Law. The Law states that, At constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its volume at 0oc for every one degree rise or fall in temperature.”
Mathematically, the law can be represented as fallows;
Let ‘V0’ be the volume of given mass of gas at 0°c when temperature is increased by one degree i.e. 1°c, then volume of  gas according to Charles law would be
V=  V+ (1/273) V0         where V1 is volume of gas at 1°c
If temperature is further increased by 1°c  i.e. 1°c   +   1°c   =   2°c
Then,    V2   =   (V+(1/273) V0)   + (1/273)  V0
=  V0   + (2/273) V0
Similarly at 3°c
V3   =  V0   + (3/273)  V0
At toc
Vt   =   V0   +  (t/273) V0
Similarly if temperature is reduced to −1°c, then
V–1   =   V0  −(1/273) V0
At  −2°c
V–2   =   V0  − (2/273) V0
At  −273°c
V–273    =    V0  − (273/273) V0
=    V0 − V=  0
This means that the volume of a given mass of a gas becomes zero at −273°c. In other words, the gas will cease to exist at this temperature.
The same conclusion can also be drawn graphically. Keeping the pressure of the gas constant, a graph is plotted between temperature and volume. Upon extrapolation (produce), the graph meets temperature at −273°c. This means volume of every gas becomes zero at −273°c.
Charle’s law, may be put in another form as fallows;
Vt   =  V0   +  (t/273)  V0
Or   Vt    = (273 V0 +t V0 )/ 273
Vt    =   V0 (273+t) / 273
If 273 + t   =   T
& 273   =    T0 (on Kelvin scale)
Then,     Vt   = V0 T / T0
Or,      V/T= V0 / T0
Thus   V / T  =   constant
V / T    =  K
V  =   KT
Or     V  α  T  (at constant pressure)
Thus, Charle’s law may also be defined as, “The volume of a given mass of a gas at constant pressure is directly proportional to the absolute or Kelvin temperature.”
Let V1 be the volume of gas at temperature T1, keeping pressure constant, if temperature is increased to T2, the volume will change to V2. Then according to Charles’s law;
     V1 / T1 = V2 / T2

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