Science (English Medium) Class 11 - CBSE Question Bank Solutions

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 = 42°C, latent heat of vaporization = 2.27 × 10⁶ J kg⁻¹, and the thermal conductivity of the porous walls = 0.80 J s⁻¹ m⁻¹°C⁻¹. Calculate the temperature of water in the pitcher when it attains a constant value.

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 100 kg m⁻³, and the specific heat capacity of water = 4200 J k⁻¹g °C⁻¹. Estimate the time taken for the temperature of fall by 1.0 °C. Make any simplifying assumptions you need but specify them.

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?

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⁻¹m⁻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 metal rod of cross sectional area 1.0 cm² is being heated at one end. At one time, the temperatures gradient is 5.0°C cm⁻¹ at cross section A and is 2.5°C cm⁻¹ 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

A hole of radius r₁ is made centrally in a uniform circular disc of thickness d and radius r₂. The inner surface (a cylinder a length d and radius r₁) is maintained at a 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 if (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 thickness L₁ and L₂ and thermal conductivites K₁ and K₂. The slabs have equal cross-sectional area. Find the equivalent conductivity of the composite slab.

Figure (28-E2) 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 if 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 the 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 W m⁻¹°C⁻¹ and of copper = 390 W m⁻¹°C⁻¹.

Following 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 conductivites are K_At = 200 W m⁻¹°C⁻¹ and K_Cu = 400 W m⁻¹°C⁻¹.

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

The two rods shown in following 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 condcutivities of aluminium and copper are 200 W m⁻¹°C⁻¹ and 400 W m⁻¹°C⁻¹ respectively.

Seven rods A, B, C, D, E, F and G are joined as shown in the figure. All the rods have equal cross-sectional area A and length l. The thermal conductivities of the rods are K_A = K_C = K₀, K_B = K_D = 2K₀, K_E = 3K₀, K_F = 4K₀ and K_G = 5K₀. 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 has 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 (28-E10) (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 is 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.

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 first 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_α. 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.