Physics Thermal Properties of Matter

A calorimeter consists of 400g of water at $24°C.$ A 500g piece of copper at $100°C$ is thrown into the water and the equilibrium temperature is found to be $36.5°C.$  What is the molar heat capacity of copper in cal/mol k, given that 1 mol of copper has a mass of 63.5g? Neglect the heat capacity of the container.

An igloo, a hemispherical enclosure built of ice $\left(1.67J/m-s°C\right)$ , has as inner radius of 2.50m. The thickness of the ice is 0.5m. At what rate must thermal energy be generated to maintain the air inside the igloo at $5°C$ when the outside temperature is - $40°C?$  Ignore all thermal energy losses through the ground or by air currents.

How is latent heat related to change of state?

When phase changes happen, why do the plateaus of temperature show?

A wooden wheel having radius of 1 m is to be fitted with an iron ring around it. The diameter of the ring is 6 mm smaller than the wooden wheel. If the coefficient of linear expansion of iron is 1.2 * 10^-5/ °C, then find the minimum increase in temperature (in °C) to fit the ring on the wheel.

A hollow sphere (mass m, radius R) is put inside a hollow cone (mass m, radius 3R and semi-angle $30°$ ) as shown in the figure. The whole arrangement is rigidly fixed to the ground at the apex of the cone. Both the sphere and the cone are made of the same material (a = 10^-4/ $°C$ ). Considering that major changes in dimensions could happen only due to heating effects, find the increase in potential energy (in Joule) of the system if it's temperature is increased by   $100°C.$

A cylindrical metal rod BC of length 1 m and radius 1 cm is joint in series to another rod AB of same material and length but having twice the radius as shown in the figure.

End A is placed at a temperature of 100°C and end C is placed at 50°C temperature. Find the temperature of the junction B.

A railway track (made of iron) is laid in winter when the average temperature is $18°C.$  The track consists of sections of 12.0m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to $48°C?$  Coefficient of linear expansion of iron = 11 * $10^{-6}/°C$ .

How is the change of state related to latent heat?

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'a'. The metal sheet is heated uniformly, bya small temperature $\Delta T,$  so that its new temperature is T + $\Delta T.$  Calculate the increase in the volume of the metal box.