Question: The relationship Lf Li 1 T is an approximation
The relationship Lf = Li (1 + αΔT) is an approximation that works when the average coefficient of expansion is small. If α is large, one must integrate the relationship dL/dT =αL to determine the final length. (a) Assuming that the coefficient of linear expansion is constant as L varies, determine a general expression for the final length. (b) Given a rod of length 1.00 m and a temperature change of 100.0°C, determine the error caused by the approximation when α = 2.00 X 10-5 (°C)-1 (a typical value for a metal) and when & = 0.020 0 (°C)-1 (an unrealistically large value for comparison).
Answer to relevant QuestionsA steel wire and a copper wire, each of diameter 2.000 mm, are joined end to end. At 40.0°C, each has an unscratched length of 2.000 m; they are connected between two fixed supports 4.000 m apart on a tabletop, so that the ...A 1.00-km steel railroad rail is fastened securely at both ends when the temperature is 20.0°C. As the temperature increases, the rail begins to buckle. If its shape is an arc of a vertical circle, find the height h of the ...A 50.0-g copper calorimeter contains 250 g of water at 20.0°C. How much steam must be condensed into the water if the final temperature of the system is to reach 50.0°C?(a) Determine the work done on a fluid that expands from i to f as indicated in Figure P20.24. (b) What If? How much work is performed on the fluid if it is compressed from f to i along the same path?A sample of an ideal gas is in a vertical cylinder fitted with a piston. As 5.79 kJ of energy is transferred to the gas by heat to raise its temperature, the weight on the piston is adjusted so that the state of the gas ...
Post your question