Question

An ideal gas `(lmanda=1.5)` is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times
A. 4 times
B. 16 times
C. 8 times
D. 2 times

Answer 1

The correct option is B. 16 times

Root mean square velocity,

\(v = \sqrt\frac{2RT}{m} \Rightarrow T \propto v^2\)

\(\frac{T_2}{T_1} = \frac{V^2_2}{V_1^2} = \frac{(V_1/2)^2}{V_1} = \frac{1}{4} \) .......(i)

From TV^γ−1 = constant

\(\Rightarrow \frac{V_2}{V_1} = (\frac{T_1}{T_2})^{\frac{1}{\gamma -1}}\)

\(\frac{V_2}{V_1} = (4)^{\frac{1}{1.5-1}} = 4^2 = 16\)

Hence the gas has to be expanded by 16 times.

Answer 2

Correct Answer - B

Answer 3

Correct answer B