Chapter 21, Problem 25A

A 30-gram piece of iron is heated to $100°C$ and then dropped into cool water where the iron’s temperature drops to $30°C$. How many calories does it lose to the water? (The specific heat capacity of iron is $0.11\text{cal/g°C}$.)

To determine

Number of calories lose by iron to the water.

Answer to Problem 25A

The number of calories lose by iron to water is $Q=231\text{cal}$ .

Explanation of Solution

Given:

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

Initial temperature of iron is $100°\text{C}$

Final temperature of iron is $30°\text{C}$

Specific heat capacity of iron is, $0.11\text{cal/g}°\text{C}$

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:

The change in temperature is,

  $\Delta T=100°\text{C}-30°\text{C}=70°\text{C}$

Now, putting the values in heat transfer equation

  $\begin{array}{c}Q=mC\Delta T\\ Q=\left(30\text{g}\right)\times \left(0.11\text{cal/g}°\text{C}\right)\times \left(70°\text{C}\right)\\ =231\text{cal}\end{array}$

Conclusion:

Therefore, the number of calories lose by iron to water is $Q=231\text{cal}$ .