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Iron Nail Heating: Finding Temperature After 15J Transfer

Chapter 3, Problem 81P

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QUESTION:

An iron nail with a mass of 12 g absorbs 15 J of heat. If the nail was initially at \(28\ ^{\circ}\mathrm{C}\), what is its final temperature?

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QUESTION:

An iron nail with a mass of 12 g absorbs 15 J of heat. If the nail was initially at \(28\ ^{\circ}\mathrm{C}\), what is its final temperature?

ANSWER:

 

Step 1 of 2

Given :

mass of iron nail = 12 g

Heat absorbed = 15 J.

Initially temperature of nail = \(28^{\circ} \mathrm{C}\)

Final temperature = ?

To calculate the final temperature, we need specific heat of iron :

The Specific Heat of Iron = \(0.440 \mathrm{J} / \mathrm{g} /{ }^{\circ} \mathrm{C}(\mathrm{K})\)

Now, let’s calculate the change in temperature (\(\Delta T\)) :

\(\begin{array}{l} \Rightarrow \mathrm{Q}(\text { Amount of heat })=\mathrm{m} \text { (mass }) \times \mathrm{C}(\text { Specific heat }) \times \Delta T \text { (Temperature change }) \\ \Rightarrow 15 \mathrm{~J}=12 \mathrm{~g} \times 0.44 \mathrm{~J} / \mathrm{g} /{ }^{\circ} \mathrm{C} \times \Delta T \\ \Rightarrow 15 \mathrm{~J}=5.28 \Delta T \\ \Rightarrow \Delta T=\frac{15}{5.28} \\ \quad=2.84^{\circ} \mathrm{C} \end{array}\)

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Iron Nail Heating: Finding Temperature After 15J Transfer
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Discover the process of determining the final temperature of an iron nail after heat absorption. Using the specific heat capacity of iron and the heat transfer formula, we calculate the temperature increase and reveal the nail's new thermal state. This tutorial offers a clear understanding of how materials respond to heat.


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