Q. 13

# A spherical shell is heated. The volume changes according to the equation V_{θ} = V_{0} (1 + γθ). Does the volume refer to the volume enclosed by the shell or the volume of the material making up the shell?

Answer :

When heated, the volume of a spherical shell varies according to the equation V_{θ} = V_{0} (1 + γθ). As the volume of spherical shell expands with rise of temperature, the volume referred here is volume of the material used to make up the shell. Here, the coefficient of expansion of volume is γ.

Rate this question :

Show that moment of inertia of a solid body of any shape changes with temperature as I = I_{1}(1 + 2αθ), where I, is the moment of inertia at 0°C and α is the coefficient of linear expansion of the solid.

A circular disc made of iron is rotated about its axis at a constant velocity ω. Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from 20°C to 50°C keeping the angular velocity constant. Coefficient of linear expansion of iron = 1.2 × 10^{–3} °C^{–1}.

A steel wire of cross-sectional area 0.5 mm^{2} is held between two fixed supports. If the wire is just taut at 20°C, determine the tension when the temperature falls to 0°C. Coefficient of linear expansion of steel is 1.2 × 10^{–5} °C^{–1} and its Young’s modulus is 2.0 × 10^{11} N m^{–2}.

A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C. Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10^{–5} °C^{–1}.

A steel ball initially at a pressure of 1.0 × 10^{5} Pa is heated from 20°C to 120°C keeping its volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel = 12 × 10^{–6} °C^{–1} and bulk modulus of steel = 1.6 × 10^{13} N m^{–1}.

A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0°C. It is filled completely with mercury at this temperature. When the temperature is raised to 10°C, 1.6 cm^{3} of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5 × 10^{–6} °C^{–1}.

Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10^{–6} °C^{–1} and 23 × 10^{–6} °C^{–1} respectively.

A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10^{–6} °C^{–1}.