Does a body at 20°C radiate in a room, where the room temperature is 30°C? If yes, why does its temperature not fall further?

Why does blowing over a spoonful of hot tea cools it? Does evaporation play a role? Does radiation play a role?

On a hot summer day we want to cool our room by opening the refrigerator door and closing all the windows and doors. Will the process work?

On a cold winter night you are asked to sit on a chair. Would you like to choose a metal chair or a wooden chair? Both are kept in the same lawn and are at the same temperature.

Two identical metal balls one at T1 = 300 K and the other at T2 = 600 K are kept at a distance of 1m in vacuum. Will the temperatures equalize by radiation? Will the rate of heat gained by the colder sphere be proportional to as may be expected from the Stefan’s law?

An ordinary electric fan does not cool the air, still it gives comfort in summer. Explain.

The temperature of the atmosphere at a high altitude is around 500°C. Yet an animal there would freeze to death and not boil. Explain.

Standing in the sun is more pleasant on a cold winter day than standing in shade. Is the temperature of air in the sun considerably higher than that of the air in shade?

Cloudy nights are warmer than the nights with clean sky. Explain.

Why is a white dress more comfortable than a dark dress in summer?

The thermal conductivity of a rod depends on

In a room containing air, heat can go from one place to another

A solid at temperature T₁ is kept in an evacuated chamber at temperature T₂ > T₁. The rate of increase of temperature of the body is proportional to

The thermal radiation emitted by a body in proportional of Tⁿ where T is its absolute temperature. The value of n is exactly 4 for

Two bodies A and B having equal surface areas are maintained at temperatures 10°C and 20°C. The thermal radiation emitted in a given time by A and B are in the ratio

One end of a metal rod is kept in a furnace. In steady state, the temperature of the rod.

Newton’s law of cooling is a special case of

A hot liquid is kept in a big room. Its temperature is plotted as a function of time. Which of the following curves may represent the plot?

A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly.

A body cools down from 65°C to 60°C in 5 minutes. It will cool down from 60°C to 55°C in

One end of a metal rod is dipped in boiling water and the other is dipped in melting ice.

A blackbody does not

In summer, a mild wind is often found on the shore of a calm river. This is caused due to

A piece of charcoal and a piece of shining steel of the same surface area are kept for a long time in an open lawn in bright sun.

A heated body emits radiation which has maximum intensity near the frequency v₀. The emissivity of the material is 0.5. If the absolute temperature of the body is doubled.

A solid sphere and a hollow sphere of the same material and of equal radii are heated to the same temperature.

A uniform slab of dimension 10 cm × 10 cm × 1 cm is kept between two heat reservoirs at temperatures 10°C and 90°C. The larger surface areas touch the reservoirs. The thermal conductivity of the material is 0.80 W m^–1 °C^–1. Find the amount of heat flowing through the slab per minute.

A liquid-nitrogen container is made of a 1 cm thick Styrofoam sheet having thermal conductivity 0.025 J s^–1m^–1°C^–1. Liquid nitrogen at 80 K is kept in it. A total area of 0.80 m² is in contact with the liquid nitrogen. The atmospheric temperature is 300 K. Calculate the rate of heat flow from the atmosphere to the liquid nitrogen.

The normal body-temperature of a person is 97°F. Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47°F, surface of the body under clothes = 1.6 m², conductivity of the cloth = 0.04 J s–¹ m^–1 °C^–1, thickness of the cloth = 0.5 cm.

Water is boiled in a container having a bottom of surface area 25 cm², thickness 1.0 mm and thermal conductivity 50W m^–1 °C^–1. 100g of water is converted into steam per minute in the steady state after the boiling starts. Assuming that no heat is lost to the atmosphere, calculate the temperature of the lower surface of the bottom. Latent heat of vaporization of water = 2.26 × 10⁶ J kg^–1.

One end of a steel rod (K = 46 J s^–1 m^–1 °C^–1) of length 1.0 m is kept in ice at 0°C and the other end is kept in boiling water at 100°C. The area of cross-section of the rod is 0.04 cm². Assuming no heat loss to the atmosphere, find the mass of the ice melting per second. Latent heat of fusion of ice = 3.36 × 10⁵ J kg^–1.

An icebox almost completely filled with ice at 0°C is dipped into a large volume of water at 20°C. The box has walls of surface area 2400 cm², thickness 2.0 mm and thermal conductivity 0.06 W m^–1 °C^–1. Calculate the rate at which the ice melts in the box. Latent heat of fusion of ice = 3.4 × 10⁵ J kg^–1.

A pitcher with 1 mm thick porous walls contains 10 kg of water. Water comes to its outer surface and evaporates at the rate of 0.1 g s^–1. The surface area of the pitcher (one side) = 200 cm². The room temperature = 45°C, latent heat of vaporization = 2.27 × 10⁶ J kg^–1, and the thermal conductivity of the porous walls = 0.80 J s^–1m^–1 °C^–1. Calculate the temperature of water in the pitcher when it attains a constant value.

A steel frame (K = 45 W m^–1 °C^–1) of total length 60 cm and cross-sectional area 0.20 cm², forms three sides of a square. The free ends are maintained at 20°C and 40°C. Find the rate of heat flow through a cross-section of the frame.

Water at 50°C is filled in a closed cylindrical vessel of height 10 cm and cross-sectional area 10 cm². The walls of the vessel are adiabatic but the flat parts are made of 1 mm thick aluminium (K = 200 J s^–1 m^–1 °C^–1). Assume that the outside temperature is 20°C. The density of water is 1000 kg m^–3, and the specific heat capacity of water = 4200 J k^–1 m^–1 °C^–1. Estimate the time taken for the temperature to fall by 1.0°C. Make any simplifying assumptions you need but specify them.

The left end of a copper rod (length = 20 cm, area of cross-section = 0.20 cm²) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation, find

(a) the temperature at a point 11 cm from the left end and

(b) the heat current through the rod. Thermal conductivity of copper = 385 W m^–1 °C^–1.

The ends of a metre stick are maintained at 100°C and 0°C. One end of a rod is maintained at 25°C. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?

A cubical box of volume 216 cm³ is made up to 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is 5°C in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.

Figure shows water in a container having 2.0 mm thick walls made of a material of thermal conductivity 0.50 W m^–1 °C^–1. The container is kept in a melting ice bath at 0°C. The total surface area in contact with water is 0.05 m². A wheel is clamped inside the water and is coupled to a block of mass M as shown in the figure. As the block goes down, the wheel rotates. It is found that after some time a steady state is reached in which the block goes down with a constant speed of 10 cm s^–1 and the temperature of the water remains constant at 1.0°C. Find the mass M of the block. Assume that the heat flows out of the water only through the walls in contact. Take g = 10 m s^–2.

On a winter day when the atmospheric temperature drops to –10°C, ice forms on the surface of a lake.

(a) Calculate the rate of increase of thickness of the ice when 10 cm of ice is already formed.

(b) Calculate the total time taken in forming 10 cm of ice. Assume that the temperature of the entire water reaches 0°C before the ice starts forming. Density of water = 1000 kg m^–3, latent heat of fusion of ice = 3.36 × 10⁵ J kg^–1 and thermal conductivity of ice = 1.7 W m^–1 °C^–1. Neglect the expansion of water on freezing.

Consider the situation of the previous problem. Assume that the temperature of the water at the bottom of the lake remains constant at 4°C as the ice forms on the surface (the heat required to maintain the temperature of the bottom layer may come from the bed of the lake). The depth of the lake is 1.0 m. Show that the thickness of the ice formed attains a steady state maximum value. Find this value. The thermal conductivity of water = 0.50 Wm^–1 °C^–1. Take other relevant data from the previous problem.

Three rods of lengths 20 cm each and area of cross-section 1 cm² are joined to form a triangle ABC. The conductivities of the rods are K_AB = 50 J s^–1 m^–1 °C^–1, K_BC = 200 J s^–1 m^–1 °C^–1 and K_AC = 400 J s^–1 m^–1 °C^–1. The junctions A, B and C are maintained at 40°C, 80°C and 80°C respectively. Find the rate of heat flowing through the rods AB, AC and BC.

A semicircular rod is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Fid the ratio of the heat transferred through a cross-section of the semicircular rod to the heat transferred through a cross-section of the straight rod in a given time.

A metal rod of cross-sectional area 1.0 cm³ is being heated at one end. At one time, the temperature gradient is 5.0°C cm^–1 at cross-section A and is 2.5°C cm^–3 at cross-section B. calculate the rate at which the temperature is increasing in the part AB of the rod. The heat capacity of the part AB = 0.40 J°C^–1, thermal conductivity of the material of the rod = 200 W m^–1 °C^–1. Neglect any loss of heat to the atmosphere.

Steam at 120°C is continuously passed through a 50 cm long rubber tube of inner and outer radii 1.0 cm and 1.2 cm. The room temperature is 30°C. Calculate the rate of heat flow through the walls of the tube. Thermal conductivity of rubber = 0.15 J s^–1 m^–1 °C^–1.

A hole of radius r₁ is made centrally in a uniform circular disc of thickness d and radius r₂. The inner surface (a cylinder of length d and radius r₁) is maintained at ta temperature θ₁ and the outer surface (a cylinder of length d and radius r₂) is maintained at a temperature θ₂(θ₁ > θ₂). The thermal conductivity of the material of the disc is K. Calculate the heat flowing per unit time through the disc.

A hollow tube has a length ℓ, inner radius R₁ and outer radius R₂. The material has a thermal conductivity K. Find the heat flowing through the walls of the tube

(a) the flat ends are maintained at temperature T₁ and T₂(T₂> T₁)

(b) the inside of the tube is maintained at temperature T₁ and the outside is maintained at T₂.

A composite slab is prepared by pasting two plates of thicknesses L₁ and L₂ and thermal conductivities K₁ and K₂. The slabs have equal cross-sectional area. Find the equivalent conductivity of the composite slab.

Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross-sectional area. The free end of the copper rod is kept at 0°C and that of the steel rod is kept at 100°C. Find the temperature at the junction of the rods. Conductivity of copper = 390 W m^–1 °C^–1 and that of steel = 46 W m^–1 °C^–1.

An aluminium rod and a copper rod of equal length 1.0 m and cross-sectional area 1 cm² are welded together as shown in figure. One end is kept at a temperature of 20°C and the other at 60°C. Calculate the amount of heat taken out per second from the hot end. Thermal conductivity of aluminium = 200 Wm^–1 °C^–1 and of copper = 390 Wm^–1 °C^–1.

Figure shows an aluminium rod joined to a copper rod. Each of the rods has a length of 20 cm and area of cross-section 0.20 cm². The junction is maintained at a constant temperature 40°C and the two ends are maintained at 80°C. Calculate the amount of heat taken out from the cold junction in one minute after the steady state is reached. The conductivities are K_Al = 200 W m^–1°C^–1andK_Cu = 400 W m^–1 °C^–1.

Consider the situation shown in figure. The frame is made of the same material and has a uniform cross-sectional are everywhere. Calculate the amount of heat flowing per second through a cross-section of the bent part if the total heat taken out per second from the end at 100°C is 130J.

Suppose the bent part of the frame of the previous problem has a thermal conductivity of 780 J s^–1m^–1 °C^–1, whereas it is 390 J s^–1m^–1°C^–1for the straight part. Calculate the ratio of the rate of hat flow through the bent part to the rate of heat flow through the straight part.

A room has a window fitted with a single 1.0 m × 2.0 m glass of thickness 2 mm.

(a) Calculate the rate of heat flow through the closed window when the temperature inside the room is 32°C and that outside is 10°C.

(b) The glass is now replaced by two glass panes, each having a thickness of 1 mm and separated by a distance of 1 mm.

Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = 1.0 J s^–1m^–1 °C^–1and that of air = 0.025 J s^–1m^–1 °C^–1.

The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.

The three rods shown in figure have identical geometrical dimensions. Heat flows from the hot end at a rate of 40 W in the arrangement

(a) Find the rates of heat flow when the rods are joined as in arrangement (b) and in (c). Thermal conductivities of alumimium and copper are 200 W m^–1 °C^–1 and 400 W m^–1 °C^–1 respectively.

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length cross-sectional area and thermal conductivity of each rod are ℓ, A and K respectively. The ends A, E and F are maintained at temperatures T₁, T₂ and T₃ respectively. Assuming no loss of heat to the atmosphere, final the temperature at B.

Seven rods A, B, C, D, E, F and G are joined as shown in figure. All the rods have equal cross-sectional area A and length ℓ. The thermal conductivities of the rods are K_A = K_C = K_D, K_D = 2K_D, K_E = 3K_D, K_F = 4K_D and K_D = 5K_D. The rod E is kept at a constant temperature T₁ and the rod G is kept at a constant temperature T₂(T₂> T₁).

(a) Show that the rod F ahs a uniform temperature T = (T₁ + 2T₂)/3.

(b) Find the rate of heat flowing from the source which maintains the temperature T₂.

Find the rate of heat flow through a cross-section of the rod shown in figure (θ₂> θ₁). Thermal conductivity of the material of the rod is K.

A rod of negligible heat capacity has length 20 cm, area of cross-section 1.0 cm² and thermal conductivity 200 W m^–1 °C^–1. The temperature of one end is maintained at 0°C and that of the other end is slowly and linearly varied from 0°C to 60°C in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes.

A hollow metallic sphere of radius 20 cm surrounds a concentric metallic sphere of radius 5 cm. The space between the two spheres in filled with a nonmetallic material. The inner and outer spheres are maintained at 50°C and 10°C respectively and it is found that 100 J of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the spheres.

Figure shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross-section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.

Two bodies of masses m₁ and m₂ and specific heat capacities s₁ and s₂ are connected by a rod of length ℓ, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the firs body is T₁ and the temperature of the second body is T₂(T₂> T₁). Find the temperature difference between the two bodies at time t.

An amount n (in moles) of a monatomic gas at an initial temperature T₀ is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature T_s(>T₀) and the atmospheric pressure is p_a. Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all changes to be slow, find the distance moved by the piston in time t.

Assume that the total surface area of a human body is 1.6 m² and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is 37°C. Stefan constant σ is 6.0 × 10⁻⁸ W m⁻² K⁻⁴.

Calculate the amount of heat radiated per second by a body of surface area 12 cm² kept in thermal equilibrium in a room at temperature 20°C. The emissivity of the surface = 0.80 and σ = 6.0 × 10⁻⁸ W m⁻² K⁻⁴.