✰ Coefficient of cubical expansion of a metal cube is γ.
✰ The volume of the cube increases by 5%.
✠ Increase in its temperature ΔT.
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
∴ Increase in its temperature ΔT =
0.05/γ
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:
_______________________________
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
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Answers & Comments
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:
_______________________________
Verified answer
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