Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping

Prove that beta equal 2 alpha and prove that gamma equal 3 alpha.

Prove that beta equal 2 alpha and prove that gamma equal 3 alpha.


2 Answers

25763 Points
2 years ago
Denote by 
α : the coefficient of linear expansion 
β : the coefficient of surface expansion 
γ : the coefficient of volumetric expansion 

Then a length increases as 

L → L ( 1 + α ΔT) 

But this means that for isotropic (same in every direction) expansion a surface (length x length) increases as 

A → A ( 1 + α ΔT)( 1 + α ΔT) ≈ A (1 +2 α ΔT) 
where we have neglected the (usually very small) square term (α ΔT)² . 

Comparing with the (definition of β) expression

A → ( 1 + βΔT) , we see the relation 

β = 2α . 


V → V ( 1 + γ ΔT) from the definition of volumetric expansion coefficient. 
But also we can approximate (volume = length x length x length) 

V → V ( 1 + α ΔT)³ ≈ V ( 1 + 3 α ΔT) , neglecting higher powers of α ΔT. 

γ = 3 α
Hope it helps
Sai Soumya
99 Points
2 years ago
You can find the answer in class 11 NCERT book in the chapter Kinetic Theory of Gases.
It has been briefly explained 
Otherwise you can refer to any reference book 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy


Get your questions answered by the expert for free