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.

A liquid of coefficient of cubical expansion $\gamma$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is filled in a container having coefficient of linear expansion $\frac{\gamma }{3}.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> On heating, liquid level in the container will

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.

Reason R : On heating, the length of the rod increases.

In the light of the above statements, choose the correct answer from the options given below:

At what temperature a gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter. 6.241cm? Both the diameters have been measured at room temperature (27°C).

(Given : coefficient of linear thermal expansion of gold a_L = 1.4 × 10^-5 K^-1)

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.

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.