Question

Derive alpha =1/T in ideal gas equation

Answer 1

$\mathfrak{\huge{\underline{Answer:}}}$

•According to Charles Law

at constant pressure and constant number of moles , volume of gas is directly proportional to the temperature of gas .

i.e: V α T

→V = kT , where k is proportionality constant or Boltzmann constant

T is taken in Kelvin , but when we use the temperature in Celsius then T = t+273

Hence,

V = k(t + 273)

at t = 0, V' = k × 273

→K =$\frac{V'}{273}$

V =$\frac{V'}{t+273}$

= V'(1 + t/273)

So let, α =$\frac{1}{273}$ { α is known as temperature coefficient }

V = V'( 1 + αt )

→$\frac{V}{V'}$= 1 + αt

→$\frac{V-V'}{V'}=αt</p><p>→V'α =\frac{V-V'}{t}$