The initial temperature of a copper sphere is 25 degreesCelsius. When the sphere

Question

The initial temperature of a copper sphere is 25 degreesCelsius. When the sphere is heated to 100 degrees Celsius thevolume of the sphere expands to 78.750 milliliters. a. What was the original volume of the sphere? Note; theanswer must be given to three decimals. b. What is the correct value of the coefficient of volumetricexpansion used in the solution of this problem? The initial temperature of a copper sphere is 25 degreesCelsius. When the sphere is heated to 100 degrees Celsius thevolume of the sphere expands to 78.750 milliliters. a. What was the original volume of the sphere? Note; theanswer must be given to three decimals. b. What is the correct value of the coefficient of volumetricexpansion used in the solution of this problem?

Explanation / Answer

The initial temperature of the copper sphere ist1= 25 degrees Celsius. When the sphere is heated to t2= 100 degreesCelsius the volume of the sphere expands to V = 78.750milliliters. a.Let the original volume of the sphere beVo,therefore,we get V1 = Vo* (1 + t1)-------------------(1) Similarly,the volume of the sphere when it is heated is V2 = Vo* (1 + t2)------------------(2) Substracting equation (1) from equation (2),we get V2 - V1= [Vo* (1 +t2) - Vo* (1 +t1)] or V = Vo * * (t2 -t1) or Vo= (V/ * (t2 -t1)) --------------------(3) Here,V = 78.750 milliliters = 78.750 *10-3 liters = 78.750 * 10-3 *10-3m3, = 51 * 10-6/K,t2= 100 oC = (100 + 273) K = 373 K andt1= 25 oC = (25 + 273) K = 298 K Substituting the above values in equation (3),we get Vo= (78.750 * 10-3/51 * 10-6* (373 - 298)) or Vo= 20.6 m3 = 20.6 * 103liters b.The correct value of the coefficient of volumetric expansionused in the solution of this problem is = 51 *10-6 /K.

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