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Question
Figure shows graphs of pressure vs density for an ideal gas at two temperatures T1 and T2.
Options
T1 > T2
T1 = T2
T1 < T2
Any of the three is possible.
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Solution
T1 > T2
The straight line T1 has greater slope than T2. This means \[\frac{P}{\rho}\] ratio is greater for T1 than T2. Now, rms velocity of a gas is given by \[\sqrt{\frac{3P}{\rho}}\] . This means rms velocity of gas with T1 molecules is greater than T2 molecules. Again, gas with higher temperature has higher rms velocity.
So, T1 > T2.
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