A rod 1.3 m long consists of a 0.8 m length of aluminum joined end to end to a 0.5 m length of brass. The free end of the aluminum section is maintained at 150°C and the free end of the brass piece is maintained at 20°C. No heat is lost through the side of the rod. At steady state what is the temperature of the point when two metals are joined? [K_al = 205 W/mK, K_b = 110 W/mK]

Ans: 90°C

The element of an electric fire with an output of 1.5 Kw is a cylinder of 0.3 m long and 0.04 m in radius. Calculate its temperature if it behaves as a black body.

Ans: 770k

A bar 0.2 m in length and of cross-sectional area 2.5 x 10^-4m² is ideally lagged. One end is maintained at 373 K while the other is maintained at 273 K by immersing in melting ice Calculate the rate at which the ice melts owing to the flow of heat along the bar.

Ans: 1.5 x 10^-4 kg/sec

A slab of stone of area 0.36 m² and thickness 10 cm is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour, 4.8 kg of ice is melted. Calculate the thermal conductivity of the stone. 

Ans: 1.244 watt m^-1k^-1

A metal rod of length 20cm and cross sectional area of 3.14 cm² is covered with non-conducting substance. One of its end is maintained at 100°C, while the other end is put in ice at 0°C. It is found that 25 grams of ice melts in 5 minutes. Calculate the thermal conductivity of the metal.

Ans: 178.3 watt m^-1k^-1

Estimate the rate of heat loss through a glass window of area 2m² and thickness 4mm when the temperature of the room is 300K and the temperature outside is 5°C.

Ans: Given, K = 1.2 Wm^-1 K^-1, 13200 Watt

Find the rate of radiation of energy from a human body of total surface area 1.5m² and a surface temperature 32°C if the surrounds are at a temperature of 22°C and the emissivity of human body is 0.94.

Ans: 88 Watt

A bar 0.2m in length and 2.5 cm² in cross section is ideally lagged. One end is maintained at 100°C and the other end is maintained at 0° C by immersing, in Melting ice. Calculate the mass of ice melt in one hour, Thermal conductivity of the material of the bar is 4 x 10^-2 Wm^-1 K^-1.

Ans: 5.36 x 10^-5kg

The Sun is a black body of surface temperature of about 6000K. If Sun's radius is 7 x.10⁸, calculate the energy per second, radiated from its surface. The Earth is about 1.5 x 10¹¹ m from the Sun. Assuming all the radiation from the Sun falls on the surface of sphere of this radius, estimate the energy per second per meter² received by the Earth.

Ans: 4.55 x 10²⁶ W, 1609 Wm^-2

A sphere of radius 2.00 cm with a black surface is cooled and then suspended in a large evacuated enclosure with black walls maintained at 27°C. If the rate of change of thermal energy of the sphere is 1.85JS^-1 when its temperature is -73°C, calculate the value of Stefan's Constant.

Ans: 5.66 x 10^-8 Wm^-2K^-4

Estimate the power loss through the unit area from a perfectly black body at 327°C to the surrounding environment at 27°C.

Ans: 6889.05 W

A spherical blackbody of radius 5 cm has its temperature of 127°C and its emissivity is 0.6. Calculate its radiant power.

Ans: 27.34 W

Estimate the radiant power loss from a human body at a temperature of 38.5°C to the environment at 0°C if the surface area of the body is 1.5 m² and its emissivity is 0.6.

Ans: 197 W

A pot with a steel bottom 8.5 mm thick rest on a hot stove. The area of the bottom of the pot is 0.15m². The water inside the pot is at 100°c and 390 g of water is evaporated every 3 minutes. Find the temperature of lower surface of the pot which is in contact with the stove. [k = 50.2 W/mk, L_v = 2256 x 10³ J/Kg]

Ans: 105°C

A man, the surface area of whose skin is 2m² is sitting in a room where the air temperature is 20°C. If his skin temperature is 37°C, find the rate at which his by loses heat. The emissivity of his skin is 0.97.

Ans: 206 w