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प्रश्न
Give its
(i) mathematical expression
(ii) graphical representation and
(iii) significance.
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उत्तर
(i) mathematical expression
suppose a gas occupies volume V1 when its pressure is P1; then
`"V"_1 ∝ 1/"P"_1 "or" "V"_1 = "k"/"P"_1`
`"P"_1"V"_1 = "k" = "constant"`
If V2 is the volume ocuupied when the pressure is P2 at the same temperature, the
`"V"_2 ∝ 1/"P"_2 "or" "V"_2 = "k"/"P"_2`
`"P"_2"V"_2 = "k" = "constant"`
`"P"_1"V"_1 = "P"_2"V"_2 = "k"` at constant temperature.
This is called Boyle's law equation.
(ii) graphical representation
The law can be verified by plotting a graph
(a) V vs `1/p` (b) V vs P (c) PV vs P
(a) V vs `1/p`: a straight line passing through the origin is obtained
(b) V vs P: a hyperbolic curve in the first quadrant is obtained
(c) PV vs P: a straight line is obtained parallel to the pressure axis.
(iii) Significance
On increasing pressure, volume decreases. The gas becomes denser. Thus at a constant temperature, the density of a gas is directly proportional to its pressure.
Atmospheric pressure is low at high altitudes, so air is less dense. Hence, a lesser quantity of oxygen is available for breathing. This is the reason why mountaineers have to carry oxygen cylinders with them.
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संबंधित प्रश्न
Explain Why?
Inflating a balloon seems to violate Boyle's law.
State the law which is represented by the following graph:
At constant temperature, the effect of change of pressure on the volume of a gas was as given below:
|
Pressure in atmosphere |
Volume in liters |
|
0.20 |
112 |
|
0.25 |
89.2 |
|
0.40 |
56.25 |
|
0.60 |
37.40 |
|
0.80 |
28.10 |
|
1.00 |
22.4 |
(a) Plot the following graphs
- P vs V
- P vs 1/V
- PV vs P
Interpret each graph in terms of the law.
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