Solving School Physics Problem: Understanding Water Heat Capacity

When it comes to physics problems in school, the concept of specific heat capacity can often be a bit of a mystery. A common problem that students face is understanding how to calculate the amount of mass of a substance when the amount of energy absorbed is known. This article will guide you through the process of solving such a problem step-by-step, demystifying the concepts of specific heat, energy absorption, and temperature change.

Understanding Specific Heat Capacity

Firstly, let's break down what specific heat capacity means. Specific heat capacity (or simply, specific heat) is a measure of the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is symbolized by the letter cc. The unit of specific heat capacity is typically J/(g°C) or J/(kg°C), where J stands for joules, g for grams, and kg for kilograms.

Simple Problem: Calculating Water Mass

Let's consider the problem presented in the original statement: an unknown mass of water with a specific heat of 4.18 J/g°C and an initial temperature of 40°C, which absorbed 300 J of energy and was heated up to 50°C. The goal is to determine the mass of water in the sample. Here’s a systematic approach to solve this problem:

Given Information:

Energy absorbed (Q) 300 J Specific heat capacity (c) 4.18 J/g°C Temperature increase (ΔT) 50°C - 40°C 10°C

Step-by-Step Solution:

The formula used to solve this problem is:

Energy (Q) Specific Heat (c) × Mass (m) × Temperature Change (ΔT)

Translating this into the given problem, we have:

300 J 4.18 J/g°C × m × 10°C

To find the mass (m), we rearrange the formula as follows:

300 J (4.18 J/g°C × 10°C) × m

300 J 41.8 J/g × m

m 300 J / 41.8 J/g

m ≈ 7.17 g

Thus, the mass of water in the sample is approximately 7.17 grams.

Why is This Important?

Understanding the concept of specific heat capacity and how to apply it in solving problems is crucial for students in advanced science classes. It offers practical applications in real-world situations such as cooking, manufacturing, and even environmental studies. For instance, specific heat capacity is used to predict the cooling process of foods, the efficiency of materials in thermal insulation, and the behavior of substances in changing temperatures.

Conclusion

By breaking down the problem into clear, manageable steps and using the correct physical relationships, it is possible to solve seemingly complex physics problems like the one discussed here. Whether you are a student grappling with academic challenges, or someone interested in the practical applications of these principles, gaining a thorough understanding of specific heat capacity and its applications is invaluable.

Frequently Asked Questions (FAQs)

What is the difference between specific heat and heat capacity? Specific heat is defined as the specific heat capacity, which is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. Heat capacity, on the other hand, is the total amount of heat required to raise the temperature of the entire substance by one degree Celsius. How does specific heat relate to temperature change? The specific heat of a substance determines how much heat is needed to change its temperature. Higher specific heat means more heat is required for the same temperature change, and vice versa. What is the significance of Joules in the unit of specific heat? Joules are a unit of work or energy. In the context of specific heat, they represent the amount of energy required to raise a unit mass of the substance by one degree Celsius.

With this knowledge, you should be well-equipped to tackle similar physics problems and appreciate the relevance of these concepts in everyday life.