0.1 m³ of water at 80°C is mixed with 0.3 m³ of water at 60°C. The final temperature of the mixture is

• 65°C

• 70°C

• 60°C

• 75°C

Which of the following statement does not hold good for thermal radiation ?

• The wavelength changes when it travels from one medium to another

• The frequency changes when it travels from one medium to another

• The speed changes when it travels from one medium to another

• They travel in straight line in a given medium

The amount of heat energy radiated by a metal at temperature T is E. When the temperature is increased to 3T, energy radiated is

• 81E

• 9E

• 3E

• 27E

The surface temperature of the stars is determined using

• Planck's law

• Wien's displacement law

• Rayleigh-Jeans law

• Kirchhoff's law

Two slabs are of the thicknesses d₁ and d₂. Their thermal conductivities are K₁ and K₂ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures θ₁ and θ₂. Assume θ₁ > θ₂. The temperature θ of their common junction is

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

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

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

• $\frac{{\mathrm{K}}_1{\mathrm{\theta }}_1 \hspace{0.17em}+ {\mathrm{K}}_2{\mathrm{\theta }}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

Hot water cools from 60°C to 50°C in the first 10 min and to 42°C in the next 10 min. Then the temperature of the surroundings is

• 20°C

• 30°C

• 15°C

• 10°C

67.

A perfect gas at 27°C is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be

• 600°C

• 327°C

• 54°C

• 300°C

Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is thrice that of C and half ofthat of A. The effective thermal conductivity of the system will be (K_A is the thermal conductivity of rod A)

• $\frac{1}{3} {\mathrm{K}}_{\mathrm{A}}$

• 3 K_A

• 2 K_A

• $\frac{2}{3} {\mathrm{K}}_{\mathrm{A}}$

The quantities of heat required to raise the temperatures of two copperspheres of radii r₁ and r₂ (r₁ = 1.51 r₂) through 1 K are in the ratio of

• $\frac{27}{8}$

• $\frac{9}{4}$

• $\frac{3}{2}$

• 1

Which one of the following is v-T graph for perfectly black body ? v_m is the frequency of radiation with maximum intensity. T is the absolute temperature.

• A

• B

• C

• D