Question

A piece of metal weighs $45 \, g$ in air and $25 \, g$ in a liquid of density $1.5 \times 10^3 \, kg-m^{-3}$ kept at $30^{\circ} C$. When the temperature of the liquid is raised to $40^{\circ}C$, the metal piece weighs $27\, g$. The density of liquid at $40^{\circ}C$ is $1.25 \times 10^3 \, kg-m^{-3}$. The coefficient of linear expansion of metal is

• A. $1.3 \times 10^{-3}/^{\circ} C $
• B. $5.2 \times 10^{-3}/^{\circ} C $
• C. $2.6 \times 10^{-3}/^{\circ} C $
• D. $0.26 \times 10^{-3}/^{\circ} C $

Answer 1

The Correct Option is C

The volume of the metal at $30^{\circ} C$ is $V_{30} = \frac{\text{loss of weight}}{\text{specific gravity} \times g }$ $ = \frac{ 45- 25 \,g}{1.5 \times g} = 13.33 \, cm^{3}$ Similarly, volume of metal at $40^{\circ} C $ is $ V_{40} = \frac{40 - 27 \,g}{1.25 \times g}$ $ = 14.40 \, cm^{3}$ Now, $ V_{40 } = V_{30} 1 + \gamma t_{2} - t_{1}$ Or $ \gamma = \frac{V_{40} - V_{30}}{V_{30} t_{2} - t_{1}} $ $ = \frac{14.40 - 13.33}{13.33 40 - 30 } $ $ = 8.03 \times 10^{-3} /^{\circ}C$ $\therefore$ Coefficient of linear expansion of the metal is $ a = \frac{\gamma}{3} = \frac{8.03 \times 10^{-3}}{3}$ $ \approx 2.6 \times 10^{-3} /^{\circ}C$

Answer 2

Thermal expansion is a phenomenon that may be seen in solids, liquids, and gases. When heat is applied to a body, it expands. Thermal expansion is the ability of an item to change dimension due to heat, either in length, density, area, or volume. When a material is heated, its kinetic energy increases. 

Thermal expansion is of three types:

• Linear expansion
• Area expansion or Superficial expansion
• Volume expansion or Cubical expansion

Linear expansion

When a solid is heated and its length increases, then the expansion is called linear expansion.

The formula of linear expansion is given by

ΔL = ɑL₀ΔT

Where

• ΔL is the change in length
• L₀ is the original length
• ΔT is the change in temperature
• ɑ is the coefficient of linear expansion.

Area expansion

When a solid is heated and its area increases, then the expansion is called area expansion.

The formula of area expansion is given by

ΔA = ꞵA₀ΔT

Where

• ΔA is the change in area
• A₀ is the original area
• ΔT is the change in temperature
• ꞵ is the coefficient of area expansion.

Volume expansion

When a solid is heated and its volume increases, then the expansion is called volume expansion.

The formula of volume expansion is given by

ΔV = ℽV₀ΔT

Where

• ΔV is the change in length
• V₀ is the original length
• ΔT is the change in temperature

ℽ is the coefficient of linear expansion.