The Question is from neet-physics thermal-properties-of-matter thermal-expansion-of-gases, and it was created by the author Mr. ANIL KUMAR.G

Question

A rigid container of volume $V$ contains $n$ moles of an ideal gas at temperature $T$. A small hole is made in the container, and the gas slowly leaks out isothermally.  Which of the following correctly describes the change in the product of pressure and volume ($PV$) as the gas leaks?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: 2
## CONCEPT FRAMEWORK
 **Primary Concept**: Ideal Gas Law and Isothermal Processes
 **Related Topics**: Moles, Pressure, Volume, Temperature
 **Prerequisites**: Understanding of the ideal gas law ($PV = nRT$) and isothermal processes (constant temperature).
## SOLUTION PATHWAY
**Given Information**:
  * Volume of container: $V$ (constant)
  * Number of moles initially: $n$
  * Temperature: $T$ (constant, isothermal process)
  * Gas leaks slowly and isothermally
**Method & Steps**:
 1. Apply the ideal gas law:
  Reasoning: The ideal gas law relates pressure, volume, number of moles, and temperature. Since the process is isothermal, the temperature remains constant.
  Formula/Rule: $PV = nRT$
 2. Analyze the change in $PV$ as gas leaks:
  Working: As the gas leaks, the number of moles ($n$) decreases.  Since $V$, $R$, and $T$ are constant, $PV$ is directly proportional to $n$. Therefore, as $n$ decreases, $PV$ decreases linearly.
  Key Point: The proportionality is linear because the relationship is directly proportional. This is the key to understanding the correct option.
 3. Identify the correct option:
  Result: $PV$ decreases linearly with the number of moles.
  Verification: The ideal gas law directly supports this conclusion.  If we halve the number of moles, we halve the $PV$ product.
 ## OPTION ANALYSIS
[A] :x: PV remains constant.: This is incorrect because the number of moles changes, and therefore the pressure changes while volume remains constant.
[B] ✓: PV decreases linearly with the number of moles.: This is the correct option, as explained above.
[C] :x: PV decreases exponentially with the number of moles.: This would only be true if the rate of leakage depended on the amount of gas present in a non-linear way, which is not the case here. 
[D] :x: PV increases linearly with the number of moles.: This is incorrect; the leakage decreases the number of moles and consequently the pressure.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing isothermal with adiabatic processes: Remember that in an isothermal process, temperature remains constant, while in an adiabatic process, no heat exchange occurs.
  2.Incorrectly applying the ideal gas law: Ensure you understand the relationship between all variables and how changes in one affect the others.
 **Quick Tips**:
  1.For isothermal processes, focus on the direct relationship between $PV$ and $n$.
  2.Visualize the process: Imagine the gas slowly escaping; the pressure must decrease proportionally to the number of moles.

Mr. ANIL KUMAR.G · Answer

PV remains constant.

Mr. ANIL KUMAR.G · Answer

The correct Option is "PV decreases linearly with the number of moles."

Mr. ANIL KUMAR.G · Answer

PV decreases exponentially with the number of moles.

Mr. ANIL KUMAR.G · Answer

PV increases linearly with the number of moles.

NEET Physics Thermal Properties Of Matter Thermal Expansion Of Gases MCQs

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