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
Answers
answer : option (2) v
RMS speed of an ideal gas is given as,
v = √{3P/ρ}
where P is pressure and ρ is density of ideal gas.
a/c to question,
T is keeping constant.
we know, P = ρRT/M
means, pressure is directly proportional to density. [ here T is constant.]
if we increase the pressure, density also increase with the same rate.
then, P/ρ always remains constant.
⇒ √{3P/ρ} remains constant.
hence, rms speed of the ideal gas remains same. i.e., v
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