A hot body is allowed to cool. The surrounding temperature is constant at 30°C. The takes time t₁ to cool from 70°C to 68°C and time t₂ to cool from 60°C to 59.5°C. Then

• t₂ = t₁

• t₂ = 2t₁

• ${\mathrm{t}}_2 = \frac{1}{2} {\mathrm{t}}_1$

• t₂ = 4t₁

A, B and C are the three identical conductors but made from different materials. They are kept in contact as shown

Their thermal conductivities are K, 2K and $\frac{\mathrm{K}}{2}$. The free end of A is at 100°C and the free end of C is at 0°C. During steady state, the temperature of the junction of A and B is nearly

• 37°C

• 71°C

• 29°C

• 63°C

A solid cylinder of radius R made of a material of thermal conductivaty K₁ is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K₂. The two ends of the combined system are maintained at two different temperatures. Then there is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

• K₁ + K₂

• $\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

• $\frac{2{\mathrm{K}}_1 + {\mathrm{K}}_2}{4}$

• $\frac{{\mathrm{K}}_1 + 3{\mathrm{K}}_2}{4}$

Two stars A and B radiate maximum energy at the wavelength of 360 nm and 480 nm respectively. Then the ratio of the surface temperatures of A and B is

• 3 : 4

• 81 : 256

• 4 : 3

• 256 : 81

In anomalous expansion of water, at what temperature, the density of water is maximum ?

• 4°C

• < 4°C

• > 4°C

• 10°C

1 g of ice is mixed with 1 g of steam. At thermal equilibrium, the temperature of the mixture is

• 50°C

• 0°C

• 55°C

• 100°C

Water is heated from 0° C to 10° C, then its volume

• does not change

• decreases

• first decreases and then increases

• increases

A pan filled with hot food cools from 94°C to 86°C in 2 min. When the room temperature is 20°C. Howl ong will it cool from 74°C to 66°C ?

• 2 min

• 2.8 min

• 2.5 min

• 1.8 min

Four rods of same material with different radii r and length l are used to connect two heat reservoirs at different temperature. Which one will conduct most heat ?

• r = 1 cm, l = 1 m

• r = 1 cm, l = $\frac{1}{2} \mathrm{m}$

• r = 2 cm, l = 2 m

• r = 2 cm, l = $\frac{1}{2} \mathrm{m}$

One kilogram of ice at 0°C is mixed with one kilogram of water at 80°C. The final temperature of the mixture is (take : specific heat of water = 4200 Jkg^-1 K^-1, latent heat of ice = 336 kJ kg^-1).

• 40°C

• 60°C

• 0°C

• 50°C