Question:hard
An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules 3 times ? (\(γ = 1.5\))
An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules 3 times ? (\(γ = 1.5\))
Show Hint
v_rms is proportional to sqrt(T), and for adiabatic change T V^(gamma-1) is constant.
Updated On: Oct 1, 2026
- \(32\) times
- \(16\) times
- \(8\) times
- \(81\) times
Show Solution
The Correct Option is D
Solution and Explanation
Step 1: Link speed and T
Three times lower speed gives nine times lower T.
Step 2: Adiabatic law
$T_1V_1^{0.5} = T_2V_2^{0.5}$, so $(V_2/V_1)^{0.5} = 9$.
Step 3: Solve
$V_2/V_1 = 81$. Option (D).
Final Answer:
Option (D). \[ \boxed{81} \]
Three times lower speed gives nine times lower T.
Step 2: Adiabatic law
$T_1V_1^{0.5} = T_2V_2^{0.5}$, so $(V_2/V_1)^{0.5} = 9$.
Step 3: Solve
$V_2/V_1 = 81$. Option (D).
Final Answer:
Option (D). \[ \boxed{81} \]
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