(I) An ideal gas expands isothermally, performing 4.30 x 10 3 J of work in the process. Calculate the heat absorbed during this expansion.

Hey, everyone in this problem, we're asked to calculate the heat absorbed by a perfect gas that undergoes an isothermal expansion performing 3.75 multiplied by 10 to the exponent three joules of work. As we're looking for the heat absorbed, we have four answer choices of Js option A 3.75 multiplied by 10 to the exponent three. Option B 4.55 multiplied by 10 to the exponent three. Option C 6.71 multiplied by 10 to the exponent three. And option D 8.82 multiplied by 10 to the exponent three. Now, I think about this problem, it seems like we aren't given a lot of information, but the key here is that we have an isothermal expansion because we have an isothermal expansion and we have this perfect gas. So we can assume that it's ideal. It tells us that the change in internal energy dealt to you will be equal to zero. OK. Again, because we have isothermal expansion of an ideal gas. Now, we know the change in internal energy is equal to zero. We're given some information about work. We wanna find the heat how can we relate those three quantities? We'll recall the change in internal energy delta U is equal to the heat Q minus the work done. W so we have two of these values. We wanna find the third simple equation. OK. So we have zero is equal to the heat Q minus the work done. W we can rearrange and write that the heat Q must be equal to the work done. OK? Now we know the work done. We're given that in the problem 3.75 multiplied by 10 to the exponent three joules. And so because we had an isothermal expansion of an ideal gas, the change in internal energy was zero, that meant that the heat absorbed is equal to the work. OK. And so the correct answer here is going to be option a 3.75 multiplied by 10 to the exponent three joules. That's it for this one. Thanks everyone for watching. See you in the next video.

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22. The First Law of Thermodynamics

First Law of Thermodynamics

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22. The First Law of Thermodynamics

First Law of Thermodynamics

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Problem 32b

Textbook Question

(I) An ideal gas expands isothermally, performing 4.30 x 10³ J of work in the process. Calculate the heat absorbed during this expansion.

Verified step by step guidance

Step 1: Understand the process described in the problem. The gas expands isothermally, meaning the temperature remains constant throughout the process. For an ideal gas undergoing an isothermal process, the first law of thermodynamics simplifies to ΔU = 0, where ΔU is the change in internal energy.

Step 2: Recall the first law of thermodynamics: ΔU = Q - W, where Q is the heat absorbed by the system and W is the work done by the system. Since ΔU = 0 for an isothermal process, the equation simplifies to Q = W.

Step 3: Identify the given values in the problem. The work done by the gas during the expansion is W = 4.30 × 10³ J. Since Q = W for an isothermal process, the heat absorbed by the gas will be equal to the work done.

Step 4: Substitute the given value of W into the equation Q = W. This will allow you to calculate the heat absorbed during the expansion.

Step 5: Conclude that the heat absorbed by the gas is numerically equal to the work done, as per the relationship Q = W in an isothermal process. Ensure units are consistent and properly expressed in joules (J).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law is fundamental in understanding gas behavior under various conditions, particularly during processes like expansion or compression.

Isothermal Process

An isothermal process occurs at a constant temperature, meaning that any heat added to the system is used to do work rather than change the internal energy. For an ideal gas, this implies that the internal energy remains constant, and the heat absorbed by the gas equals the work done by the gas. This concept is crucial for calculating heat transfer in thermodynamic processes.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of an isothermal expansion, this law can be expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. Since the internal energy change is zero in an isothermal process, the heat absorbed equals the work done.

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(I) An ideal gas expands isothermally, performing 4.30 x 103 J of work in the process. Calculate the heat absorbed during this expansion.

Key Concepts

Ideal Gas Law

Isothermal Process

First Law of Thermodynamics

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(I) An ideal gas expands isothermally, performing 4.30 x 10³ J of work in the process. Calculate the heat absorbed during this expansion.