Analisis Gas Ideal: Kalor, Volume, Dan Usaha

Guys, let's dive into the fascinating world of ideal gases! This problem gives us a real-world scenario where a system of ideal gas absorbs heat, leading to a change in volume while maintaining constant pressure. We'll break down the concepts involved, apply the relevant formulas, and arrive at the correct answers. This isn't just about formulas; it's about understanding how energy transforms in a gas system. We will explore how a gas performs work when it expands against a constant pressure. We'll also see how the heat absorbed is related to the change in internal energy and the work done. The interplay of these concepts is fundamental to understanding thermodynamics, and we will get to explore how to solve them.

Memahami Konsep Dasar Gas Ideal

First, let's get our fundamentals right. An ideal gas is a theoretical concept that helps us simplify and understand the behavior of real gases under certain conditions. It's a gas where the particles (atoms or molecules) are assumed to have no volume and don't exert any forces on each other (except during collisions). This might sound a bit abstract, but it's a very useful starting point! These assumptions let us use simple equations to describe the relationship between pressure, volume, temperature, and the amount of gas.

In our case, the gas absorbs heat, and that absorption is going to change things. Think of it like this: when you add heat to a gas, you're giving the gas molecules more energy. This extra energy can manifest in different ways. It can increase the kinetic energy of the molecules, which would lead to a higher temperature (if the volume is constant). Or, as in our case, it can be used to do work if the gas expands against an external pressure. It's like adding fuel to a fire; the fire will either burn hotter, expand the volume it takes up, or both! It all depends on how the energy is allowed to move within the system.

Now, let’s talk about the key things involved here: heat, volume, and work. Heat is the energy transferred between a system and its surroundings due to a temperature difference. The volume of the gas is how much space it takes up, and the work is the energy the gas does to expand. In our problem, we know the gas absorbs some heat and its volume changes. That means we have the information to calculate the work done by the gas. The gas will expand from a smaller volume to a larger one due to the absorption of energy as heat.

Perhitungan Usaha yang Dilakukan Gas

Okay, let's put our thinking caps on and tackle the math. The problem gives us the heat absorbed (4 × 10⁴ J), the initial volume (0.35 m³), the final volume (0.50 m³), and the constant pressure (200 kPa or 200,000 Pa). We need to figure out the work done by the gas. Remember, when a gas expands against constant pressure, the work done is given by a simple formula: W = P × ΔV, where W is the work, P is the pressure, and ΔV is the change in volume.

So, first things first, let's calculate the change in volume (ΔV). This is simply the final volume minus the initial volume: ΔV = 0.50 m³ - 0.35 m³ = 0.15 m³. Now we have all the pieces we need, and calculating the work is easy! Just plug the values into our formula. The pressure is 200,000 Pa, and the change in volume is 0.15 m³.

Therefore, W = 200,000 Pa × 0.15 m³ = 30,000 J. So the gas does 30,000 Joules of work. That means out of the 40,000 Joules of heat energy it absorbed, 30,000 Joules of that energy went directly into doing work by expanding the volume of the gas against constant pressure, which is a significant amount of the total energy! The remaining energy goes to the change in internal energy, which we will not calculate here, but it is important to understand. It is the core of understanding thermodynamics!

Analisis Energi dalam Sistem

Now, let's step back and look at the bigger picture of energy transfer in this system. According to the first law of thermodynamics, the change in internal energy (ΔU) of a system equals the heat added to the system (Q) minus the work done by the system (W). This can be written as: ΔU = Q - W. In this case, we know the heat absorbed (Q = 40,000 J) and the work done by the gas (W = 30,000 J). This means we can find the change in internal energy.

So, ΔU = 40,000 J - 30,000 J = 10,000 J. The change in internal energy is positive, which makes sense! The gas has absorbed more energy than it used to do work, and the rest is stored within the gas molecules. The change in internal energy can also be viewed as the increase in kinetic energy of the gas molecules. This also implies that the temperature of the gas must have increased since the internal energy has increased.

It is important to understand how the heat added, the work done, and the change in internal energy are all connected. They are all energy in different forms. Heat is the energy that is being added to the system. Work is the energy that is being done by the system, and the change in internal energy is the remaining energy within the system. Understanding all of these concepts will make solving these types of problems much easier!

Kesimpulan dan Jawaban yang Benar

In summary, for our ideal gas system, we have: the work done is 30,000 J, and the change in internal energy is 10,000 J. The most important thing here is to understand the concepts and the formula. The formulas will allow you to do calculations. The concepts will help you understand what is going on. With the concepts, you can easily adapt when the situations change. You should always think through the process of what is going on, and from there, you will be able to answer the question.

Now, let's look back at the original question to make sure we've covered everything. We have calculated the work done, and we have discussed the change in internal energy, so we have all the information that we need. We're now equipped to choose the correct answers based on our calculations and understanding of the concepts.