Chapter 2: Problem 122

A \(100.0\) -g block of iron and a \(100.0\) -g block of aluminum are both initially at \(25.0^{\circ} \mathrm{C}\). Both are then warmed to \(100.0^{\circ} \mathrm{C}\). Does one block require more heat energy than the other to reach \(100.0{ }^{\circ} \mathrm{C}\) ? If so, how much more?

Short Answer

Expert verified

The aluminum block requires an additional 3337.5 J of heat energy to reach 100.0 °C compared to the iron block. This is because the aluminum has a higher specific heat capacity, which means it takes more heat energy to change its temperature by the same amount compared to iron.

Step by step solution

Determine the given values

We are given the following values: - Mass of iron (\(m_{Fe}\)) = 100.0 g - Mass of aluminum (\(m_{Al}\)) = 100.0 g - Initial temperature (\(T_i\)) = 25.0 °C - Final temperature (\(T_f\)) = 100.0 °C - Specific heat capacity of iron (\(c_{Fe}\)) = 0.450 J/g°C - Specific heat capacity of aluminum (\(c_{Al}\)) = 0.897 J/g°C

Calculate the change in temperature

To calculate the change in temperature for both the iron and the aluminum blocks, we subtract the initial temperature from the final temperature: \(\Delta T = T_f - T_i = 100.0 °C - 25.0 °C = 75.0 °C\)

Calculate the heat energy for the iron block

Now, we will use the values for the mass, specific heat capacity, and change in temperature of the iron block to compute the heat energy required to warm it to 100.0 °C: \(q_{Fe} = m_{Fe} \times c_{Fe} \times \Delta T = (100.0 \,\text{g}) \times (0.450 \,\text{J/g°C}) \times (75.0 \, °C) = 3375 \, \text{J}\)

Calculate the heat energy for the aluminum block

Similarly, we will compute the heat energy required to warm the aluminum block to 100.0 °C: \(q_{Al} = m_{Al} \times c_{Al} \times \Delta T = (100.0 \,\text{g})\times (0.897\,\text{J/g°C}) \times (75.0\,°C) = 6712.5 \,\text{J}\)

Compare the heat energies and determine the difference

It is clear from the calculations that the aluminum block requires more heat energy to reach 100.0 °C than the iron block: \(6712.5\,\text{J} > 3375\,\text{J}\) To find out how much more heat energy the aluminum block requires, we subtract the heat energy for the iron block from that of the aluminum block: \(\Delta q = q_{Al} - q_{Fe} = 6712.5\,\text{J} - 3375\,\text{J} = 3337.5\,\text{J}\) Therefore, the aluminum block requires an additional 3337.5 J of heat energy to reach 100.0 °C compared to the iron block.

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A \(100.0\) -g block of iron and a \(100.0\) -g block of aluminum are both initially at \(25.0^{\circ} \mathrm{C}\). Both are then warmed to \(100.0^{\circ} \mathrm{C}\). Does one block require more heat energy than the other to reach \(100.0{ }^{\circ} \mathrm{C}\) ? If so, how much more?

Short Answer

Step by step solution

Determine the given values

Calculate the change in temperature

Calculate the heat energy for the iron block

Calculate the heat energy for the aluminum block

Compare the heat energies and determine the difference

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