Calculating Temperature Rise in Iron Using Specific Heat

The concept of specific heat is fundamental in thermodynamics, allowing us to understand how different materials respond to changes in heat energy. In this article, we'll walk through a practical example involving 100 grams of iron, providing a detailed calculation for the temperature rise when it receives a specific amount of heat energy. We’ll also cover the necessary notation and units to ensure the correctness of the calculation.

Proper Notation and Units

Before delving into the calculation, it's crucial to use the correct and precise notation, especially in scientific contexts like thermodynamics. Below are the correct notations and symbols:

The symbol for degrees Celsius is deg;C, not just C. The correct symbol for joule is J, not Joul. A required space is necessary before a unit symbol, such as "450 J/kg K" instead of "450J/kg K". The symbol for kelvin is K, not k. To avoid confusion with complex unit symbols, it's recommended to group them in parentheses, as in "J/kg K".

Calculation Example

The given problem is as follows: If 100 grams of iron at 20 deg;C is given 2250 J of heat energy, what will its temperature rise to, with the specific heat of iron being 450 J/kg K?

Step-by-Step Solution

To solve this problem, we need to use the formula for heat energy:

Q m * c * Delta;T

Where:

Q is the heat energy (2250 J). m is the mass of the substance (100 grams, which is 0.1 kg). c is the specific heat capacity (450 J/kg K). Delta;T is the change in temperature, which we need to find.

First, we need to rearrange the formula to solve for the change in temperature:

Delta;T Q / (m * c)

Now, substituting the given values:

Delta;T 2250 J / (0.1 kg * 450 J/kg K)

Delta;T 2250 J / 45 J/K

Delta;T 50 K

The change in temperature (Delta;T) is 50 K. Since 1 K is equivalent to 1 deg;C, the temperature rise is 50 deg;C.

Practical Applications and Further Study

This example highlights the importance of understanding specific heat and how it affects the temperature of materials when heat is added. Understanding these concepts is crucial in various fields, including thermodynamics, engineering, and environmental science. By mastering the calculations, you can better predict and control temperature changes in real-world applications.

For a deeper dive, you can explore additional resources in your class notes and textbooks. These materials will provide comprehensive coverage of thermodynamic principles and problem-solving techniques, ensuring a solid foundation in the subject.