How do you derive the Ideal Gas Law from Boyle and Charles’ laws?

Question

Boyle’s law says that PV = constant, provided temperature (T) is constant.

Charles’ law says that V/T = constant, provided that pressure (P) is constant.

The problem is: my physics and chemistry textbooks then declare that “combining the two laws together, you get VP/T = constant (the ideal gas law). But they never bother to explain exactly how it is derived from those two. Does anyone know how the two are combined to get it?

Answer 1

The ideal gas law is actually PV=nRT where n is number of moles and R is the constant .0821 atm*L/mol*K. If you are solving for the constant, you would get R=PV/nT.

Answer 2

consider a system with pressure p1,temp.t1&volumev1.assume that it changes into system 2 ofpressurep2,volumev2&temp.t2 while undergoing a sytem of pressure p2,volume-v&temp.t2.

then according to boyle's law

p1v1=p2v.

v =p1v1/p2

now keeping pressure const. by charle's law

v/t1=v2/t2

v =v2t1/t2.

now equating v we get

p1v1/t1 =p2v2/t2

pv/t=r           {r-constant

pv =rt

if the gas has n moles

PV=nRT               {R-universal gas const.}