Heat Loss: Cooling 1 Kg Water (100°C To 0°C)

Hey guys! Ever wondered how much energy is released when you cool down water? It's a fascinating topic that dives into the world of thermodynamics, specifically the concept of heat capacity. Let's break down the calculation of heat loss when cooling 1 kg of water from boiling point (100°C) to freezing point (0°C). We'll use the specific heat capacity of water, which is a key factor in understanding this process. Let's dive in and make things crystal clear!

Understanding Specific Heat Capacity

First off, specific heat capacity is a crucial concept here. What exactly is it? Well, it's the amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius (or 1 Kelvin). Water has a relatively high specific heat capacity, which means it takes a good amount of energy to change its temperature. This is why water is so effective at regulating temperatures, like in our bodies or in large bodies of water like oceans. The specific heat capacity of water is approximately 4.18 Joules per gram per degree Celsius (J/g°C). This value is what we'll use in our calculation.

The Formula for Heat Transfer

To calculate the heat lost or gained, we use a simple yet powerful formula:

Q = mcΔT

Where:

• Q is the heat energy transferred (in Joules)
• m is the mass of the substance (in grams)
• c is the specific heat capacity of the substance (in J/g°C)
• ΔT is the change in temperature (in °C)

This formula basically tells us that the amount of heat energy (Q) is directly proportional to the mass (m), the specific heat capacity (c), and the temperature change (ΔT). The larger the mass, the higher the specific heat capacity, or the greater the temperature change, the more heat energy is involved. Keep this in mind, as we'll be putting this formula to work shortly to solve our problem about the cooling water.

Applying the Formula to Our Problem

Alright, let's get to the heart of the matter! We want to find out how much heat 1 kg of water loses when it cools from 100°C to 0°C. We already know the specific heat capacity of water (4.18 J/g°C), but we need to make sure our units are consistent. Since the specific heat is given in terms of grams, we'll convert 1 kg to grams: 1 kg = 1000 g. The temperature change (ΔT) is the final temperature minus the initial temperature, which is 0°C - 100°C = -100°C. The negative sign indicates that the water is losing heat.

Step-by-Step Calculation

Now, let's plug the values into our formula:

Q = mcΔT

Q = (1000 g) * (4.18 J/g°C) * (-100°C)

Q = -418000 J

So, the water loses 418000 Joules of heat. The negative sign simply tells us that the heat is being lost by the water to the surroundings.

Analyzing the Result

Our calculation shows that 1 kg of water loses a whopping 418000 Joules of heat when cooled from 100°C to 0°C. This is a significant amount of energy! It highlights the remarkable ability of water to store and release heat, thanks to its high specific heat capacity. Think about it – this is why large bodies of water can moderate climates, preventing drastic temperature swings. Also, consider how this principle is used in various applications, from cooling systems in cars to industrial processes. The high heat capacity of water makes it an invaluable substance in many aspects of our lives.

Choosing the Correct Answer

Looking back at the options, the correct answer is D) 418000 J. It’s crucial to understand the underlying principles and the formula to arrive at the correct answer. This isn't just about memorizing a number; it's about grasping the physics behind heat transfer. By understanding how specific heat capacity works, you can apply this knowledge to solve a variety of problems related to thermodynamics and heat exchange. Remember, physics is all about understanding the world around us, and this example perfectly illustrates how the seemingly simple act of cooling water involves a significant amount of energy transfer.

Real-World Applications of Heat Transfer

Understanding heat transfer isn't just for textbooks and exams; it's super relevant to everyday life! Think about how your car's radiator works – it uses water to absorb heat from the engine and dissipate it into the air, preventing the engine from overheating. That’s the specific heat capacity of water in action! Or consider cooking: when you boil water to cook pasta, you're using the water's ability to absorb a large amount of heat without drastically increasing in temperature, allowing the pasta to cook evenly. Even the climate is heavily influenced by the heat capacity of water. Oceans act as giant heat reservoirs, absorbing heat in the summer and releasing it in the winter, which helps to moderate temperatures in coastal regions. These are just a few examples of how the principles of heat transfer play a vital role in various aspects of our daily routines and the environment.

The Importance of Water's High Specific Heat Capacity

Let’s really dig into why water’s high specific heat capacity is such a big deal. Imagine if water had a low specific heat capacity, like, say, metal. The temperature of water would change much more rapidly with the addition or removal of heat. This would mean that our bodies, which are mostly water, would be much more susceptible to temperature fluctuations. A small change in the surrounding temperature could lead to drastic changes in our body temperature, which, as you can imagine, wouldn’t be great for our health. Similarly, the oceans and lakes would experience much larger temperature swings, which would have a devastating impact on marine life. The stable temperature environment provided by water's high specific heat capacity is essential for the survival of countless organisms and the overall balance of our planet's ecosystems. It truly underscores the unique and crucial role water plays in sustaining life as we know it. Water's specific heat capacity is one of the reasons Earth is such a habitable planet. Think about it! We owe a lot to this amazing property of water!

Conclusion: Heat Loss Calculation

So, to wrap things up, we've successfully calculated the amount of heat lost when 1 kg of water cools from 100°C to 0°C. We found that the water loses 418000 Joules of heat. This calculation highlights the significance of water's specific heat capacity and its role in various real-world applications. By understanding these fundamental principles, we can better appreciate the amazing properties of water and its importance in our lives and the environment. Remember the formula, Q = mcΔT, and you'll be able to tackle similar problems with confidence. Keep exploring the fascinating world of physics! There's always something new to learn, and the more you understand, the more you'll appreciate the science that governs our world.