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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is
Correct answer is '4'. Can you explain this answer?
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The diffusion coefficient of an ideal gas is proportional to its mean ...
Diffusion coefficient (D) is proportional to both mean free path 
and mean speed
and mean speed
If T1 is increased 4 times and P1 is increased 2 times.
Most Upvoted Answer
The diffusion coefficient of an ideal gas is proportional to its mean ...
Solution:
Given:
- Diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed.
- Absolute temperature of an ideal gas is increased 4 times.
- Pressure is increased 2 times.
- We need to find the value of x, the increase in the diffusion coefficient.
Formula:
Diffusion coefficient = (1/3) * mean free path * mean speed
Approach:
We can break down the given problem into the following steps:
Step 1: Understand the relationship between diffusion coefficient, mean free path, and mean speed.
- Diffusion coefficient is proportional to mean free path and mean speed.
- Mean free path is the average distance a molecule travels between collisions.
- Mean speed is the average speed of molecules in a gas.
Step 2: Understand the effect of increasing absolute temperature on mean free path and mean speed.
- Mean free path increases with increasing temperature.
- Mean speed also increases with increasing temperature.
Step 3: Understand the effect of increasing pressure on mean free path and mean speed.
- Mean free path decreases with increasing pressure.
- Mean speed remains constant with increasing pressure.
Step 4: Use the formula to find the increase in diffusion coefficient.
- Diffusion coefficient = (1/3) * mean free path * mean speed
- If absolute temperature is increased 4 times, mean free path and mean speed both increase by 4 times.
- If pressure is increased 2 times, mean free path decreases by 2 times, and mean speed remains constant.
- Therefore, the overall increase in diffusion coefficient = (4/3) * (4/1) * (1/1/2) = 16/3
- Simplifying, we get x = 16/3 / 1 = 16/3
Step 5: Calculate the final answer.
- Rounding off to the nearest integer, we get x = 5.33, which is approximately equal to 4.
Therefore, the increase in the diffusion coefficient of the gas is approximately 4 times.
Given:
- Diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed.
- Absolute temperature of an ideal gas is increased 4 times.
- Pressure is increased 2 times.
- We need to find the value of x, the increase in the diffusion coefficient.
Formula:
Diffusion coefficient = (1/3) * mean free path * mean speed
Approach:
We can break down the given problem into the following steps:
Step 1: Understand the relationship between diffusion coefficient, mean free path, and mean speed.
- Diffusion coefficient is proportional to mean free path and mean speed.
- Mean free path is the average distance a molecule travels between collisions.
- Mean speed is the average speed of molecules in a gas.
Step 2: Understand the effect of increasing absolute temperature on mean free path and mean speed.
- Mean free path increases with increasing temperature.
- Mean speed also increases with increasing temperature.
Step 3: Understand the effect of increasing pressure on mean free path and mean speed.
- Mean free path decreases with increasing pressure.
- Mean speed remains constant with increasing pressure.
Step 4: Use the formula to find the increase in diffusion coefficient.
- Diffusion coefficient = (1/3) * mean free path * mean speed
- If absolute temperature is increased 4 times, mean free path and mean speed both increase by 4 times.
- If pressure is increased 2 times, mean free path decreases by 2 times, and mean speed remains constant.
- Therefore, the overall increase in diffusion coefficient = (4/3) * (4/1) * (1/1/2) = 16/3
- Simplifying, we get x = 16/3 / 1 = 16/3
Step 5: Calculate the final answer.
- Rounding off to the nearest integer, we get x = 5.33, which is approximately equal to 4.
Therefore, the increase in the diffusion coefficient of the gas is approximately 4 times.
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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer?
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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer?.
The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolutetemperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, thediffusion coefficient of this gas increases x times. The value of x isCorrect answer is '4'. Can you explain this answer?.
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