A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of AT. The Young's modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is
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![A steel rod of length L and diameter D,
fixed at both ends, is uniformly heated
to a temperature rise of AT. The
Young's modulus is E and the
coefficient of linear expansion is a.
The thermal stress in the rod is
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Ο ΕαΔΤL
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- A 5.0 L steel gas can is filled to the brim with gasoline at 10°C. Taking into account the expansion of the gas can, how much gasoline spills out when the gas and the gas can both reach 25°C when left out in the sunshine on a summer day. Given that the gas can is an isotropic solid, and that the coefficient of linear thermal expansion for steel is: 11 × 10-6 K-¹ and that the coefficient of volume thermal expansion for gasoline is 0.90 × 10-³ K-¹.A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100°C, and that of the far end of the aluminum rod is held at 0°C. If the copper rod is 0.42 m long, what must be the length of the aluminum rod so that the temperature at the junction is 50°C?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…
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