A mixture of two gases is contained in a vessel. The gas 1 is monoatomic and gas 2 is diatomic and the ratio of their molecular masses . What is the ratio of root mean square speeds of the molecules of two gases?
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Official Solution
Correct Option: (1)
To find the ratio of the root mean square (RMS) speeds of the molecules of two gases, we can use the formula for the root mean square speed of gas molecules:
where:
is the root mean square speed,
is the Boltzmann constant,
is the absolute temperature, and
is the mass of the gas molecule.
The above equation can also be expressed in terms of molar mass ( ) as:
where:
is the ideal gas constant,
is the molar mass of the gas.
Given:
Gas 1 is monoatomic, and Gas 2 is diatomic.
The ratio of their molar masses .
We need to find the ratio of the RMS speeds for gases 1 and 2:
Substitute the given mass ratio:
Thus, the ratio of the root mean square speeds of the molecules of the two gases is 2, which matches with the given correct answer.
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PYQ 2018
medium
physicsID: met-2018
Two different isotherms representing the relationship between pressure and volume at a given temperature of the same ideal gas are shown for masses and of the gas respectively in the figure given, then}
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Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
From ideal gas equation . Step 2: Detailed Explanation:
For a given , . The curve with larger product at the same or corresponds to larger mass. From the figure, the curve for has higher product, so . Step 3: Final Answer:
.
03
PYQ 2018
medium
physicsID: met-2018
A gas at the temperature is contained in a closed vessel. If the gas is heated through , then percentage increase in its pressure will be
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Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
For a gas in a closed vessel (constant volume), . Step 2: Detailed Explanation:
. Step 3: Final Answer:
The percentage increase is .
