badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

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

Please check your email for login details.
MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th pass

                        

Prove that beta is equal to 2 alpha. And gamma is equal to 3 alpha

3 years ago

Answers : (3)

Arun
25311 Points
							
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 . 

Likewise 

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. 

Hence 
γ = 3 α
3 years ago
mary
13 Points
							
Using solvings show that one beta particle is equal to two alpha particle and one gamma particle is equal to one particle,simultaneously
 
one year ago
Rishi Sharma
askIITians Faculty
614 Points
							Dear Student,
Please find below the solution to your problem.

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 .

Likewise
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.
Hence
γ = 3 α

Thanks and Regards
4 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details