Question

Derive alpha v =1/T in ideal gas equation

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, $\boxed{\boxed{\bold{V_0\alpha=\frac{(V-V_0)}{t}}}}$

Answer 2

According to Charles's law

at constant pressure and 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

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