A pipe of inner radius R1, outer radius R2 and constant thermal conductivity K is maintained at an inner temperature T1 and outer temperature T2. For a length of pipe L find the rate at which the heat is lost and the temperature inside the pipe in the steady state.

An electric kettle is made out of stainless steel, weighs two pounds (when empty) and is equipped with a heating element that consumes 2 kw of electricity. assuming that the water and the kettle are at the same uniform temperature at any moment of time, calculate the shortest possible time to bring 2 quarts of water from room temperature to the onset of boiling

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.

What is the strain energy stored in a solid uniformly circular shaft of length 3.0 m and diameter 120 mm when subject to pure torsion if the maximum shear stress is 40 mpa? g-80gpa