Find the temperature distribution in a rectangular plate 10 cm by 30 cm if twoadjacent sides are held at 100◦ and the other two sides at 0◦.

A steel beam 10.0 m sits next to a concrete wall when the temperature is 30.0o If the temperature rises to 50.5o C, how large must the gap be if the steel beam just touches the concrete wall?

A container which is air tight has a volume of * 2 * 500L internal pressure of 1.0 atmosphere, internal temperature of 15 °C is washed off ythe deck of a ship located in the Philippine Trench, and sinks to a depth where the pressure is 175 atmosphere and the temperature is 3 °C. What would be the volume in m³ of the gas inside be when the container breaks under the pressure at this depth?

In this problem you will estimate the heat lost by a typical house, assuming that the temperature inside is Tin = 20°C and the temperature outside is Tout = 0°C. The walls and uppermost ceiling of a typical house are supported by 2 x 6-inch wooden beams (kwood = 0.12 W/(mK)) with fiberglass insulation (kins = 0.04 W/(mK)) in between. The true depth of the beams is actually 5.625 %3D %3D %3D inches, but we will take the thickness of the walls and ceiling to be Lwall = 18 cm to allow for the interior and exterior covering. Assume that the house is a cube of length L = 9.0 m on a side. Assume that the roof has very high conductivity, so that the air in the attic is at the same temperature as the outside air. Ignore heat loss through the ground. The effective thermal conductivity of the wall (or ceiling) keff , is the area-weighted average of the thermal conductivities of the wooden beams and the fiberglass insulation that make up each of them. Allowing for the fact that the 2 x 6 beams…