The thermo emf of a hypothetical thermocouple varies with the temperature θ of hot junction as  E = $\mathrm{a} \mathrm{\theta } + \mathrm{b} {\mathrm{\theta }}^2$ in volts, where the ratio $\frac{\mathrm{a}}{\mathrm{b}}$ is 700^o C. If the cold junction is kept at 0^o C, then the neutral temperature is

• 700^o C 

• 1400^o C

• 390^o C

• no neutral temperature is possible for this thermocouple

A current of 1.6 A is passed through a solution of CuSO_4. How many Cu⁺⁺ ions are liberated in one minute? (Electronic charge= 1.6 x 19^-19 C)

• 3 × 10²⁰

• 3 × 10¹⁰ 

• 6 × 10²⁰

• 6 × 10¹⁰

The surface temperature of the sun which has maximum energy emission at 500 nm is 6000 K. The temperature of a star which has maximum energy emission at 400 nm will be

• 8500 K

• 4500 K

• 7500 k

• 6500 K

0.1 m² of water at 80°C is mixed with 0.3 m³ of water at 60°C. The final temperature of the mixture is

• 65^o C

• 70^o C

• 60^o C

• 75^o C

A black body has a wavelength of ) λ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

• $\frac{2 \mathrm{\lambda }}{3}$

• $\frac{3 \mathrm{\lambda }}{2}$

• $\frac{4 \mathrm{\lambda }}{9}$

• $\frac{9 \mathrm{\lambda }}{4}$

50 g ice at 0°C in insulator vessel, 50 g water of 100^oC is mixed in it, then final temperature of the mixture is (neglect the heat loss)

• 10^oC

• 0^o << T_m < 20^oC

• 20^oC

• above 20^oC

The earth receives solar radiation at a rate of 8.2 J cm^-2 min^-1. If the sun radiates as the black bodies, the temperature at the surface of the sun will be (the angle subtended by sun on the earth in suppose 0.53° and Stefan constant is σ = 5.67x 10^-6 Wm³ K⁴

• 5800 K

• 6700 K

• 8000 K

• 7800 K

A slab consists of portions of different materials of same thickness and having the conductivities K₁ and K₂. The equivalent thermal conductivity of the slab is

• K₁ + K₂

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

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

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

A metal rod at a temperature of 145°C, radiates energy at a rate of 17W. If its temperature is increased to 273°C, then it will radiate at the rate of

• 49.6 W

• 17.5 W

• 50.3 W

• 67.5 W

130.

A system consist of a cylinder surrounded by a cylindrical shell. A cylinder is a radius R and is made of material of thermal conductivity K, whereas a cylindrical shell has inner radius R and outer radius ZR and is made of material of thermal conductivity twice as that of cylinder. Assuming the system in steady state and negligible heat loss across the cylindrical surface, find the effective thermal conductivity of the system, if the two ends of the combined system are maintained at two different temperatures.

• 3 K

• $\frac{2}{3}$K

• $\frac{7}{4}$K

• $\frac{5\mathrm{K}}{4}$