Question

Coefficient of cubical expansion of a metal cube is γ . Increase in temperature for which the volume of the cube increases by5% is.

Answer 1

Answer:

γ0.05

Explanation:

It is given that V 2=1.05V 1

Also, we know that V

2 =V 1(1+γΔT)

Equating , we getγΔT=0.05

So, ΔT= γ0.05

Answer 2

Given:

✰ Coefficient of cubical expansion of a metal cube is γ.

✰ The volume of the cube increases by 5%.

To find:

✠ Increase in its temperature ΔT.

Solution:

Given that:

V₂ = V₁ ( 1 + 5/100 )

V₂ = V₁ ( (100 +5)/100 )

V₂ = V₁ ( (105)/100 )

V₂ = 1.05V₁

Formula for cubical expansion:

✭ V₂ = V₁( 1 + γ ΔT ) ✭

➛ V₂ = V₁ + Vγ ΔT

➛ ΔT = (V₂ - V₁)/Vγ

➛ ΔT = 5/100γ

➛ ΔT = 0.05/γ

∴ Increase in its temperature ΔT =

0.05/γ

Additional information:

Thermal expansion means increase in the size of a substance on heating.

Volume Expansion:

➛ When a bulk solid like a cube, cuboid, sphere, cylinder, etc is heated its volume increases and thermal expansion is called volume expansion.

The amount of volume expansion ( ΔV ) depends upon:

• The original volume ( V )
• Rise in temperature ( ΔT )
• The nature of the solid material.

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