At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at 0°C?

Question

At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at 0°C? (A) 0°C (B) -273°C (C) 32°C (D) -204°C

Tardigrade Admin · Accepted Answer

νrms propto √T At 0°C , νrms propto√273 At temp. T, (νrms /2) propto √T ∴ (1/2) = (√T/√273) or T = (273/4) = 68.2 K ≈ 69 K T = 69 - 273 = - 204° C

Q. At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at $0^{\circ} C$ ?

$0^{\circ} C$

$- 27 3^{\circ} C$

$3 2^{\circ} C$

$- 20 4^{\circ} C$

$ν_{r m s} \propto T$
At $0^{\circ} C, ν_{r m s} \propto 273$
At temp. $T, \frac{ν _{r m s}}{2} \propto T$
$∴ \frac{1}{2} = \frac{T}{273}$ or $T = \frac{273}{4} = 68.2 K \approx 69 K$
$T = 69 - 273 = - 20 4^{\circ} C$

Q. At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at 0∘C?

0∘C

−273∘C

32∘C

−204∘C