Question:hard
The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at \(47^{\circ}\) C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively)
The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at \(47^{\circ}\) C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively)
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In an adiabatic change T V^(gamma-1) is constant and the r.m.s. speed goes as the square root of T.
Updated On: Oct 1, 2026
- \(47^{\circ}\) C
- \(132^{\circ}\) C
- \(320^{\circ}\) C
- \(405^{\circ}\) C
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Use pressure-volume form:
$PV^\gamma$ is constant, and $T\propto PV$, so $TV^{\gamma - 1}$ is constant.
Step 2: Substitute the numbers:
$T_2 = \frac{T_1}{9}$ gives $V_2^{0.5} = 9V_1^{0.5}$. Squaring, $V_2 = 81V_1$ (D).
Final Answer:
81 times. \[ \boxed{81\text{ times}} \]
$PV^\gamma$ is constant, and $T\propto PV$, so $TV^{\gamma - 1}$ is constant.
Step 2: Substitute the numbers:
$T_2 = \frac{T_1}{9}$ gives $V_2^{0.5} = 9V_1^{0.5}$. Squaring, $V_2 = 81V_1$ (D).
Final Answer:
81 times. \[ \boxed{81\text{ times}} \]
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