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Question 21 of 36

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SAT Subject Test

An experiment is performed to measure the specific heat of copper. A lump of copper is heated in an oven, then dropped into a beaker of water. To calculate the specific heat of copper, the experimenter must know or measure the value of all of the quantities below EXCEPT the

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mass of the water

Correct Answer: 
No

original temperatures of the copper and the water

Correct Answer: 
No

final (equilibrium) temperature of the copper and the water

Correct Answer: 
No

time taken to achieve equilibrium after the copper is dropped into the water

Correct Answer: 
Yes

specific heat of the water

Correct Answer: 
No

The correct answer is “the time taken to achieve equilibrium after the copper is dropped into the water.” When an amount of heat Q is transferred to or from a material, its magnitude is given by Q equals m c left parenthesis T subscript f end subscript minus T subscript i end subscript right parenthesis, where m is the mass of the material, c is its specific heat and T subscript f end subscript and T subscript i end subscript are its final and initial temperature, respectively. As the copper cools, heat is transferred from it to the water, which gets warmer until both the copper and water are in equilibrium at the same temperature. By conservation of energy, the heat transferred from the copper must be equal to the heat transferred to the water. To determine the specific heat of copper, the experimenter would set the expression for the heat transferred from the copper equal to that for the heat transferred to the water, and solve the equation for the specific heat of copper. Time does not appear in the expression but the quantities in the other choices do. As long as no heat is lost to the surroundings, it does not matter how long it takes to reach equilibrium. So it is not necessary to know or measure the time taken for the copper to come to equilibrium with the water.

Question Difficulty: 
medium