Question

The RMS speed of an ideal gas is v. If the pressure of the gas molecules is quadrupled while
keeping the temperature constant, then the new
RMS speed will be
(1) 2v
(2) v
(3) v/2
(4) v/4
Answer=(2)​

Answer 1

The "option (2) v" is correct.

Explanation:

RMS speed of an ideal gas is given as,

v = $\dfrac{\sqrt{3}P}{\rho}$

Where, P is pressure and ρ is density of ideal gas.

According to question,

T is taken asconstant.

We know that know,

P = $\frac{\rho\ RT}{M}$

Pressure is directly proportional to density. [ Here, T is constant.]

If we increase the pressure, density also increase with the same rate.

Then, $\frac{ P}{\rho}$ always remains constant.

⇒ √{3P/ρ} remains constant.

Hence, the RMS speed of the ideal gas remains same. i.e., v.

The "option (2) v" is correct.

Answer 2

Answer:

V is the correct answer

RMS speed is independent of pressure change

Explanation:

Hope it helps you

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