hw8.docx - Problem 6.4 Suppose two blocks of the same metal are heated The first block receives 490 calories of heat and rises 18 degrees Celsius in

# hw8.docx - Problem 6.4 Suppose two blocks of the same metal...

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Problem 6.4 Suppose two blocks of the same metal are heated. The first block receives 490 calories of heat and rises 18 degrees Celsius in temperature. The second block receives 280 calories of heat and rises 36 degrees Celsius in temperature. If the mass of the first block is 35 grams, what is the mass of the second? Solve using dimensionless ratios. To start with, this case is related to Heat Transfer . The heat content, Q, of an object depends upon its specific heat, c, and its mass, m. The Heat Transfer is the measurement of the thermal energy transferred when an object having a defined specific heat and mass undergoes a defined temperature change. Heat transfer = (mass)(specific heat)(temperature change): Q= m * c * ΔT . The proportions among the various variables can be easily seen by dividing one equation by the other and expressing the result in terms of dimensions ratios, which refers to Q 2 Q 1 = c 2 M 2 ΔT 2 c 1 M 1 ΔT 1 . In order to know the mass of the second metal, the equation can be transferred into M 2 M 1 = c 1 Q 2 ΔT 1 c 2 Q 1 ΔT 2 . Since both blocks are made of the same metal, the specific heats are the same and the ratio of c1 to c2 is equal to one. The first block receives 490 calories of heat Q 1 and rises 18 degrees Celsius ΔT 1 while the second block receives 280 degree Celsius Q 2 and rises 36 degree Celsius ΔT 2 . Therefore, M 2 = c 1 Q 2 ΔT 1 c 2 Q 1 ΔT 2 *M 1 = 280 18 490 36 *35=10g. Thus, the mass of the second metal is 10g. Problem 6.8 We have two objects and one of them is clearly iron. The second object, which is made of an unknown metal, has a mass that is one-third as great as the iron object.

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