Chapter 21, Problem 26A

Suppose a 30-gram piece of iron is dropped into a container of water and gives off 165 calories in cooling. Calculate the iron’s temperature change.

To determine

The change in temperature of iron.

Answer to Problem 26A

The change in temperature of iron piece is $\Delta T=50°\text{C}$ .

Explanation of Solution

Given:

Mass of iron piece, $m=30\text{g}$

The number of calories lose by iron to water is $Q=165\text{cal}$

Formula Used:

The heat transfer in calories is given by,

  $Q=mC\Delta T$

Where, $m$ is mass in grams, $C$ is specific heat capacity in $\text{cal/g}°\text{C}$ and $\Delta T$ is change in temperature in $°\text{C}$ .

Calculation:

As, the specific heat capacity of iron is $C=0.11\text{cal/g}°\text{C}$

Now, putting the values in heat transfer equation

  $\begin{array}{l}Q=mC\Delta T\\ 165\text{cal}=\left(30\text{g}\right)\times \left(0.11\text{cal/g}°\text{C}\right)\times \left(\Delta T\right)\\ \Rightarrow \Delta T=\frac{165}{30\times 0.11}°\text{C}\\ \Rightarrow \Delta T=50°\text{C}\end{array}$

Conclusion:

Therefore, the change in temperature of iron piece is $\Delta T=50°\text{C}$ .