Question

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity, of the cube is β and the coefficient of volume expansion is α. 

(A) [P / αβ] 

(B) [Pα / β] 

(C) [βp / α] 

(D) [αβ / p]

Answer 1

Correct option: (A) [P / αβ]

Explanation: 

Pressure applied = P

Volume elasticity = β

Coefficient of volume expansion = α

Rise in temperature be Δθ

Then   ΔV = Vα ∙ Δθ

(ΔV / V) = α ∙ Δθ        (1)

Volume elasticity = β = {P / (ΔV / V)}

from (1),

β = (P / αΔθ)

Hence    Δθ = (P / αβ)