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Chapter 5: Problem 50

Two solid objects, A and B, are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) of water at \(10.0^{\circ} \mathrm{C}\). Object A increases the water temperature by $3.50^{\circ} \mathrm{C} ; \mathrm{B}\( increases the water temperature by \)2.60{ }^{\circ} \mathrm{C}$. (a) Which object has the larger heat capacity? (b) What can you say about the specific heats of \(\mathrm{A}\) and \(\mathrm{B}\) ?

Short Answer

Expert verified
The short answer to the question is: (a) Object A has the larger heat capacity, because it causes a greater temperature increase in the water it is placed in. (b) We cannot determine the specific heats of objects A and B from the given information, as we do not have their masses and initial temperatures.

Step by step solution

01

Find the heat transferred from the objects to the water

When each object is placed in the beakers, it transfers its heat to the water, which results in a temperature increase. We can use the equation: \[Q = mc\Delta T\] where \(Q\) is the heat transfer, \(m\) is the mass, \(c\) is the specific heat, and \(\Delta T\) is the change in temperature. Since the mass and the initial temperature of the water in the beakers are the same, we can compare the heat transfers (\(Q_A\), \(Q_B\)) by comparing their temperature increases (\(\Delta T_A\), \(\Delta T_B\)). **Step 2: Calculate the heat transfer from both objects**
02

Calculate \(Q_A)\) and \(Q_B\)

From the given data, object A increases the water temperature by \(3.50^\circ \mathrm{C}\) and object B increases the water temperature by \(2.60{ }^{\circ} \mathrm{C}\). So, we can write \[\frac{Q_A}{Q_B} = \frac{\Delta T_A}{\Delta T_B}\] By plugging in the given values we get: \[\frac{Q_A}{Q_B} = \frac{3.50}{2.60}\] **Step 3: Compare the heat capacities**
03

Determine which object has a larger heat capacity

Since the ratio \(\frac{Q_A}{Q_B} > 1\), this implies that object A loses more heat than object B, therefore it has a larger heat capacity. The answer of part (a) is: Object A has the larger heat capacity. **Step 4: Determine the specific heats of objects A and B**
04

Determine if the specific heats of A and B can be compared

Specific heat is an intrinsic property of a material, meaning it is only dependent on the material itself and not the amount of the material. However, from the given data, we cannot determine the masses and initial temperatures of objects A and B, so it is impossible to compare their specific heats without more information. The answer to part (b) is: We cannot determine the specific heats of A and B from the given information.

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Most popular questions from this chapter

In a thermodynamic study, a scientist focuses on the properties of a solution in an apparatus as illustrated. A solution is continuously flowing into the apparatus at the top and out at the bottom, such that the amount of solution in the apparatus is constant with time. (a) Is the solution in the apparatus a closed system, open system, or isolated system? (b) If the inlet and outlet were closed, what type of system would it be?

Under constant-volume conditions, the heat of combustion of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is $16.49 \mathrm{~kJ} / \mathrm{g}\(. A \)3.00-\mathrm{g}$ sample of sucrose is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.94 to \(24.62^{\circ} \mathrm{C} .(\mathbf{a})\) What is the total heat capacity of the calorimeter? (b) If the size of the sucrose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

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