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Boyles law:
Boyles Law states that the product of the pressure and volume for a gas is a constant for a fixed amount of gas at a fixed temperature.
Mathematically, Boyles law can be defined as
or .
(a)
Pressure of sample of air at C is k Pa.
Volume of the gas .
Boyles law: .
Substitute corresponding values in the above formula.
.
Volume as a function of :
Consider .
Substitute in above formula.
(b)
Consider .
Differentiate with respect to on each side.
Find the value at .
.
represents rate of change of volume with respect to pressure at C.
Units of are .
(a) .
(b) .
represents rate of change of volume with respect to pressure at C and
Units of are .
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