The outer face of a rectangular slab of equal thickness of iron and brass are maintained at `100^(@)C` and `0^(@)C`, respectively. Find the temperature of the interface. The conductivities of iron and brass are 14 and 126 `W//mK` respectively.

A brass boiler has a base area of 0.15 m^2 and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min. When placed on a gas stove. Estimate the temperature of the part of the flame in contact with boiler. Thermal conductivity of brass = 109 j s^-1 m^-1 ^@C^-1 .

It is desired to make a 20.0Omega coil of wire whose temperature coefficient of resistance is zero. To do this, a carbon resistor of resistance R_(1) is placed in series with an iron resistor of resistance R_(2) . The proportion of iron and carbon are so chosen that R_(1) +R_(2)= 20 Omega for all temperatures near 20^@C . Find the values of R_(1) and R_(2). Temperature coefficient of resistance for carbon, alpha_(C)= - 0.5 xx 10^(-3)//^(@)C and that of iron is alpha_(Fe) =5 xx 10^(-3)//^(@)C.

The bottom of a container is a 4.0 cm thick glass (mu=1.5) slab. The container contains two immiscible liquids A and B of depths 6.0 and 8.0 cm respectively. What is the apparent position of a scratch on the outer surface on the bottom of the glass slab, when viewed through the container? Refractive indices of A and B are 1.4 and 1.3 respectively.

A brass and an iron rod are each of one metre long at 0^@C . Find the difference in their lengths at 100^@C . Coefficient of linear expansion of brass is 0.000019 and of iron = 0.000012.

A 10g piece of iron ( C =0.45 J//g^(@)C ) at 100^(@)C is dropped into 25g of water ( C =4.2 J//g^(@)C) at 27^(@)C . Find temperature of the rion and water system at thermal equilibrium .

If the vertices A, B, C of a triangle ABC are (1,2,3), (-1,0,0), (0,1,2) respectively, then find angleABC [ angleABC is the angle between the vectors vec(BA) and vec(BC) ]