NEET
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- NEET
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- Physics
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- Kinetic Theory of Gases
NEET · Physics · Kinetic Theory of Gases
The pressure ( P ) versus temperature ( T in Kelvin) graph for a...
The pressure () versus temperature ( in Kelvin) graph for a fixed mass of an ideal gas shows two straight lines passing through the origin, corresponding to two different constant volumes and . The line for is steeper than the line for . Two states of the gas, and , are marked on the lines for and respectively, such that both states have the exact same pressure . If and are the root mean square (rms) speeds of the gas molecules in states and respectively, which of the following is correct?
Options
- A
- B
- C
- D
Correct answer
A.
Step-by-step solution
From the ideal gas equation, .
For a graph, the slope is . Since the line for is steeper than the line for , its slope is greater, which means .
States and are at the same pressure . From the graph equation , at a constant pressure , the temperature is directly proportional to the volume. Since , the temperature of state (on ) is less than the temperature of state (on ), so .
The rms speed of gas molecules is given by . Since and , it follows that .
Answer:
For a graph, the slope is . Since the line for is steeper than the line for , its slope is greater, which means .
States and are at the same pressure . From the graph equation , at a constant pressure , the temperature is directly proportional to the volume. Since , the temperature of state (on ) is less than the temperature of state (on ), so .
The rms speed of gas molecules is given by . Since and , it follows that .
Answer: