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Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.
Correct answer is '117.75'. Can you explain this answer?
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Two containers are maintained at the same temperature and are filled w...
117-118
We know that
Average speed =
and root mean square speed =
Given that
We know that
Average speed =
and root mean square speed =
Given that
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Two containers are maintained at the same temperature and are filled w...
Given:
- Two containers are maintained at the same temperature.
- The first container is filled with an ideal gas whose molecules have mass m1.
- The second container is filled with an ideal gas whose molecules have mass m2.
- The mean speed of molecules in the second gas is 10 times the rms (root mean square) speed of the molecules in the first gas.
To find:
The ratio of m1/m2 to the nearest integer.
Formula:
The rms speed of molecules in an ideal gas is given by the formula:
vrms = sqrt(3kT/m)
where:
- vrms is the rms speed
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the mass of the molecule
Solution:
Let's assume the temperature of both containers is T.
Step 1: Find the mean speed of molecules in the second gas.
The mean speed is given by:
vmean = sqrt(8kT/(πm))
Step 2: Find the rms speed of molecules in the first gas.
We can rearrange the formula for vrms:
vrms = sqrt(3kT/m)
Step 3: Use the given information to form an equation.
The mean speed of molecules in the second gas is 10 times the rms speed of molecules in the first gas:
vmean2 = 10 * vrms1
Substituting the formulas for vmean and vrms:
sqrt(8kT/(πm2)) = 10 * sqrt(3kT/m1)
Step 4: Solve the equation for m1/m2.
Squaring both sides of the equation:
8kT/(πm2) = 100 * 3kT/m1
Simplifying:
m1/m2 = (8 * 100 * 3 * π) = 2400π
Approximating the value of π as 3.14:
m1/m2 ≈ 2400 * 3.14 ≈ 7536
Rounding to the nearest integer:
m1/m2 ≈ 7536 ≈ 117.75 (to the nearest integer)
Therefore, the ratio of m1/m2 is approximately 117.75.
- Two containers are maintained at the same temperature.
- The first container is filled with an ideal gas whose molecules have mass m1.
- The second container is filled with an ideal gas whose molecules have mass m2.
- The mean speed of molecules in the second gas is 10 times the rms (root mean square) speed of the molecules in the first gas.
To find:
The ratio of m1/m2 to the nearest integer.
Formula:
The rms speed of molecules in an ideal gas is given by the formula:
vrms = sqrt(3kT/m)
where:
- vrms is the rms speed
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the mass of the molecule
Solution:
Let's assume the temperature of both containers is T.
Step 1: Find the mean speed of molecules in the second gas.
The mean speed is given by:
vmean = sqrt(8kT/(πm))
Step 2: Find the rms speed of molecules in the first gas.
We can rearrange the formula for vrms:
vrms = sqrt(3kT/m)
Step 3: Use the given information to form an equation.
The mean speed of molecules in the second gas is 10 times the rms speed of molecules in the first gas:
vmean2 = 10 * vrms1
Substituting the formulas for vmean and vrms:
sqrt(8kT/(πm2)) = 10 * sqrt(3kT/m1)
Step 4: Solve the equation for m1/m2.
Squaring both sides of the equation:
8kT/(πm2) = 100 * 3kT/m1
Simplifying:
m1/m2 = (8 * 100 * 3 * π) = 2400π
Approximating the value of π as 3.14:
m1/m2 ≈ 2400 * 3.14 ≈ 7536
Rounding to the nearest integer:
m1/m2 ≈ 7536 ≈ 117.75 (to the nearest integer)
Therefore, the ratio of m1/m2 is approximately 117.75.
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Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer?
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Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer?.
Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer?.
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Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer?, a detailed solution for Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer? has been provided alongside types of Two containers are maintained at the same temperature and are filled with ideal gases whose molecules have mass m1 and m2 respectively. The mean speed of molecules of the second gas in 10 times the rms speed of the molecules of the first gas. Find the ratio of m1/m2 to the nearest integer.Correct answer is '117.75'. Can you explain this answer? theory, EduRev gives you an
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