Thermal Properties of Matter

Convert a temperature of 122°F into the Celsius scale.

A faulty thermometer has its ice point marked at −10° and its steam point marked at 110° on its own scale. If this thermometer reads 20°, find the actual temperature on the Celsius scale.

A steel rod of length 2 m at 20°C is heated to 120°C. Find the increase in its length. (α for steel = 1.2 × 10⁻⁵ /°C)

The side of a thin square metal plate increases by 0.5% when it is heated. Find the percentage increase in its area.

A steel wire of cross-sectional area 1 mm² is held taut between two rigid supports at 30°C. Find the tension developed in the wire when the temperature falls to 10°C. (α for steel = 1.1 × 10⁻⁵ /°C, Y = 2.0 × 10¹¹ N/m²)

A pendulum clock keeps correct time at a certain temperature. If the temperature rises by 15°C and the coefficient of linear expansion of the pendulum's material is 2 × 10⁻⁵ /°C, find the loss of time in one day (86400 s).

A glass flask filled with a liquid shows a coefficient of apparent expansion of 4 × 10⁻⁴/°C for the liquid. If the coefficient of linear expansion of the glass is 1 × 10⁻⁵/°C, find the coefficient of real expansion of the liquid.

Find the heat required to raise the temperature of 500 g of water from 20°C to 80°C. (Specific heat of water = 4200 J/kg·K)

Find the heat required to completely convert 100 g of ice at 0°C into water at 0°C. (Latent heat of fusion of ice = 80 cal/g)

200 g of water at 80°C is mixed with 300 g of water at 20°C in a container of negligible heat capacity. Find the final temperature of the mixture.

A metal slab of area 0.5 m² and thickness 2 cm has its two faces maintained at 100°C and 20°C. Find the rate of heat conduction through the slab. (K = 200 W/m·K)

Two slabs of the same length L and same cross-sectional area, having thermal conductivities K and 3K, are joined end to end (in series) between two heat reservoirs. Find the equivalent thermal conductivity of the combination.

Two rods of copper and aluminium, of the same length, with cross-sectional areas 2 cm² and 3 cm² respectively, are connected in parallel between the same two temperatures. Find the ratio of the thermal current through the copper rod to that through the aluminium rod. (K_Cu = 400 W/m·K, K_Al = 200 W/m·K)

Ice forms on the surface of a lake. If the time taken for the ice thickness to grow from x to 2x is t₁, and the time taken to grow further from 2x to 3x is t₂, find the ratio t₂ : t₁.

A body cools from 60°C to 50°C in 5 minutes, with the surrounding temperature constant at 20°C. Using Newton's law of cooling, find the time taken for the same body to cool from 50°C to 40°C.

A black body of surface area 0.1 m² is at a temperature of 27°C. Find the power radiated by it. (Stefan's constant σ = 5.67 × 10⁻⁸ W/m²K⁴; ignore the surroundings)

If the absolute temperature of a black body is doubled, find the percentage increase in the total radiant power emitted by it.

The maximum spectral emissive power of a star's surface occurs at a wavelength of 5800 Å. Find the surface temperature of the star. (Wien's constant b = 2.9 × 10⁻³ m·K)