An ideal gas (which is is a hypothetical gas that conforms to the laws governing gas behavior) confined to a container with a massless piston at the top. (Figure 2) A massless wire is attached to the piston. When an external pressure of 2.00 atm is applied to the wire, the gas compresses from 4.90 to 2.45 L. When the external pressure is increased to 2.50 atm, the gas further compresses from 2.45 to 1.96 L. In a separate experiment with the same initial conditions, a pressure of 2.50 atm was applied to the ideal gas, decreasing its volume from 4.90 to 1.96 L in one step. If the final temperature was the same for both processes, what is the difference between q for the two-step process and q for the one-step process in joules? Express your answer with the appropriate units.
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![### Part C
**Problem Statement:**
An ideal gas (which is a hypothetical gas that conforms to the laws governing gas behavior) is confined to a container with a massless piston at the top.
In **Figure 2**, a massless wire is attached to the piston. When an external pressure of 2.00 atm is applied to the wire, the gas compresses from 4.90 L to 2.45 L. When the external pressure is increased to 2.50 atm, the gas further compresses from 2.45 L to 1.96 L.
In a separate experiment with the same initial conditions, a pressure of 2.50 atm was applied to the ideal gas, decreasing its volume from 4.90 L to 1.96 L in one step.
**Question:**
If the final temperature was the same for both processes, what is the difference between \( q \) for the two-step process and \( q \) for the one-step process in joules?
**Instructions:**
Express your answer with the appropriate units.
**Available Hint:**
Click on the "View Available Hint(s)" link if you need help solving the problem.
**Input Section:**
- A space is provided for entering the value and units.
- Button to submit the answer.
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**Analysis Details:**
The problem involves understanding the behavior of an ideal gas under compression at different pressures and how this affects the heat \( q \) involved in the process. Calculations should be based on thermodynamic principles and relationships involving pressure, volume, and temperature.
**Figures and Diagrams Explanation:**
While the image mentions Figure 2, no specific diagram or graph is visible within the provided text. Explanation of any hypothetical diagrams would include showing a piston within a container and a graph illustrating the changes in volume under different applied pressures.
If further clarification on figures or diagrams is required, a hypothetical visual should include:
1. **Figure 2:**
- A container with a piston and an attached massless wire.
- Initial volume at 4.90 L.
- First compression step to 2.45 L under 2.00 atm.
- Second compression step to 1.96 L under 2.50 atm.
This breakdown serves to guide students through the thermodynamic processes described and encourages interactive engagement with the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5387081-05af-4c61-b379-73a2f6a67bdc%2Fa7052fd2-8131-4fce-9f0a-622696612de6%2Fp0qb5t_processed.jpeg&w=3840&q=75)
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