Question

prove that p∆v = ∆nRT​

Answer 1

Answer:

How do I derive pV=nRT?

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According to Boyle's law

V∝1/P

and According to Charle's law

V∝T

According to Avogadro's law

V∝n

Joining all the above equations we get,

V∝nT/P

V= constant nT/P

V= RnT/P

(R=General gas constant)

PV=nRT

This is called an Ideal gas equation or general gas equation.

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Answer 2

Answer:

Boyle’s law states that pressure P and volume V of a given mass of confined gas are inversely proportional:

P

∝

1

V

P∝1V,

while Charles’ law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure

V

∝

T

V∝T.

By combining the two laws, we get

PV

T

=

C

PVT=C,

where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).

The proportionality factor is the universal gas constant, R, i.e. C = nR.

Hence the ideal gas law

PV

=

nRT

PV=nRT.