Two liquids of specific heat ratio 1:2 are at temperature `2theta and theta`

A sphere of radius r, density, rho and specific heat s is heated to temperature theta and then cooled in an enclosure at temperature theta_(0) . How , the rate of fall of temperature is related with r, rho and s?

Mass of a body is M, its specific heat is S and temperature is T. The body is dropped in a liquid. If the mass of the liquid is m, specific heat is s and temperature is t,then prove that the final temperature of the mixture is theta=(MST+mst)/(MS+ms) . If the liquid is water then show that, S=(m(theta-t))/(M(T-theta)) .

Two liquids of masses m and 5 m at temperatures 3 theta, 4 theta are mixed, If their specific heats are 2S,3S respectively, the resultant temperature of mixture is

A liquid of mass M and specific heat s is at temperature 2t . If another liquid of same mass, specific heat 1.5 times s at a temperature of (t)/(3) is added to it, the resultant temperature will be

Two liquids A and B are at 25^(@)C and 15^(@) C. Their masses are in 2 : 3 and specific heats in ratio 3 : 4 then resultant temperature when they are mixed is

A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2 c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is

A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2 c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is