JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
In an ideal gas at temperature \(T,\) the average force that a molecule applies on the walls of a closed container depends on \(T\) as \(T^q\) . A good estimate for \(q\) is
- A \(\frac {1}{2}\)
- B \(2\)
- C \(\frac {1}{4}\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
Pressure, \(P=\frac{1}{3} \frac{m N}{V} V_{r m s}^{2}\) or, \(\quad P=\frac{(m N) T}{V}\) If the gas mass and temperature are constant then \(P \propto\left(V_{\max }\right)^{2} \propto T\) So, force \(\propto\left(V_{\text {rns }}\right)^{2} \propto T\) i.e., Value of \(q=1\)
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