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 = 151 K T2 = 151K - 273 = -122°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 $^{\circ}$ 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.
$∴ \frac{K _{1}}{K _{2}} = \frac{T _{1}}{T _{2}}$
$\Rightarrow \frac{K}{K /3} = \frac{273 + 180}{T _{2}}$
$\Rightarrow 3 = \frac{453}{T _{2}}$
$T_{2} = 151 K$
$T_{2} = 151 K - 273 = - 12 2^{\circ} C$

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