The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at 180° C is

Question

The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at 180° C is (A)  -122° C  (B)  -90° C  (C)  60° C  (D)  151° C

Tardigrade Admin · Accepted Answer

Kinetic energy of a gas is directly proportional to its temperature. ∴ (K1/K2)=(T1/T2) ⇒ (k/K/3)=(273+180/T2) ⇒ 3=(453/T2) T2=151K=151-273=-122oC

Q. The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at $180^{\circ} C$ is

$- 122^{\circ} C$

$- 90^{\circ} C$

$60^{\circ} C$

$151^{\circ} C$

Kinetic energy of a gas is directly proportional to its temperature.
$∴$ $\frac{K _{1}}{K _{2}} = \frac{T _{1}}{T _{2}}$ $\Rightarrow$
$\frac{k}{K /3} = \frac{273 + 180}{T _{2}}$ $\Rightarrow$
$3 = \frac{453}{T _{2}}$ $T_{2} = 151 K = 151 - 273 = - 122^{o} C$

Q. The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at 180∘C is

−122∘C

−90∘C

60∘C

151∘C