Chapter 12.2, Problem 22PP

To determine

The amount of thermal energy to be added to a substance for a given change in temperature.

Answer to Problem 22PP

The amount of thermal energy to be added is $6.81\times {10}^7\text{ J}$.

Explanation of Solution

Given:

The temperature of 100 kg iron is changed from $25°\text{C}$ to $1538°\text{C}$ by adding a specific amount of thermal energy.

Formula Used:

When temperature of an object is changed from $T_A$ (in Kelvin) to $T_B$ , there is always a gain or loss of thermal energy. This energy will be dependent on the temperature change, mass of the object $m$ and specific heat $C$ , and is given by the expression,

  $Q=mC\left(T_B-T_A\right)$ ..... (1)

Calculation:

Here, the given object is iron which has a mass of $m\text{=1}00\text{ kg}$ . The temperature of iron is changed from $25°\text{C}$ to $1538°\text{C}$ . The specific heat of iron is $C=450\text{ J/kg}\cdot \text{K}$ .

The initial temperature of iron in Kelvin can be calculated as,

  $\begin{array}{c}{T}_A=25+273\\ =298\text{ K}\end{array}$

Similarly, the final temperature of iron in Kelvin is,

  $\begin{array}{c}{T}_A=1538+273\\ =1811\text{ K}\end{array}$

Substituting these parameters in (1), the thermal energy to be added to achieve this temperature change is,

  $\begin{array}{c}Q=100\times 450\left(1811-298\right)\\ =6.81\times {10}^7\text{ J}\end{array}$

Conclusion:

Thus, the thermal energy required to raise the temperature of iron for the given range is $6.81\times {10}^7\text{ J}$ .