Question

Derive (alpha)
v=1/Tfor ideal gas.

Answer 1

we know, according to Charles's law 
at constant pressure and constant number of moles , volume of gas is directly proportional to the temperature of gas .
e.g., V α T 
⇒ V = kT , where k is proportionality constant .
T is in Kelvin , but when we use the temperature in °C then T = t + 273 where T is temperature in °C .
now, V = k(t + 273) 
at t = 0, V₀ = k × 273 ⇒ K = V₀/273 
now, V = V₀/273( t + 273) = V₀(1 + t/273) 
Let , α = 1/273 { α is known as temperature coefficient } 
V = V₀( 1 + αt ) 
⇒V/V₀ = 1 + αt 
⇒(V - V₀ )/V₀ = αt 
⇒V₀α = (V - V₀)/t 
Hence, \boxed{\boxed{\bold{V_0\alpha=\frac{(V-V_0)}{t}}}}V0​α=t(V−V0​)​​​