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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 Boyle's Law on the basis of the kinetic theory of matter.
Choose the correct answer:
If the pressure is doubled for a fixed mass of a gas, its volume will become
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.
(b) Assuming that the pressure values given above are correct, find the correct measurement of the volume.
561 dm3 of a gas at STP is filled in a 748 dm3 container. If the temperature is constant, calculate the percentage change in pressure required.
A certain amount of a gas occupies a volume of 0.4 litre at 17°C. To what temperature should it be heated so that its volume gets (a) doubled, (b) reduced to half, pressure remaining constant?
Calculate the volume of dry air at STP that occupies 28 cm3 at 14°C and 750 mmHg pressure when saturated with water vapour. The vapour pressure of water at 14°C is 12 mmHg.
Name or state the following:
The law which studies the relationship between pressure of a gas and the volume occupied by it at constant temperature.
Calculate the following:
Calculate the temperature at which a gas ‘A’ at 20°C having a volume, of 500 cc. will occupy a volume of 250 cc.
Assuming temperature remaining constant calculate the pressure of the gas in the following:
The pressure of a gas having volume 100 lits. originally occupying 75 dm3 at 700 mm. pressure.
State Boyle’s law
