A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner and outer surfaces are Tn and Ti, respectively. The thermal conductivity of the material of which the cylinder is made is k. Derive an equation for the rate of heat transfer P through the walls of the cylinder. Simplify this equation assuming that the thickness of the cylinder d is much smaller than the its inner radius R.

Luis and Salman are trying to increase the temperature of a substance by heating it. . What is the quantity of heat in kilojoules required to raise the temperature of 1.2 kg of the substance from3°C to 110 °C at a pressure of 1.0 atm? Please keep three significant figures. Useful information: Melting point = 293 K heat of fusion = 3.90 x 104 J/kg. boiling point is 423 K heat of vaporization 7.80 x 104 J/kg (at a pressure of 1.0 atm). The specific heats for the solid phase is 600 J/(kg K) The specific heats for the liquid phase is 1000 J/(kg K) The specific heats for the gaseous phase is 400 J/(kg K)

A solid sphere has a temperature of 799 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cube's temperature in kelvins? Number TS Units To

A closed box is filled with dry ice at a temperature of -81.3 oC, while the outside temperature is 21.5 oC. The box is cubical, measuring 0.392 m on a side, and the thickness of the walls is 4.40 × 10-2 m. In one day, 3.93 × 106 J of heat is conducted through the six walls. Find the thermal conductivity of the material from which the box is made.