At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 20° C ?

Question

At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 20° C ? (A) 40° C (B) 80° C (C) 313° C (D) 586° C

Tardigrade Admin · Accepted Answer

E propto T ∴ (E2/E1)=(T2/T1) ⇒ (2 E1/E1)=(T2/(20+273)) ⇒ T2=293 × 2=586 K =313° C

Q. At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at $2 0^{\circ} C$ ?

$4 0^{\circ} C$

$8 0^{\circ} C$

$31 3^{\circ} C$

$58 6^{\circ} C$

$E \propto T ∴ \frac{E _{2}}{E _{1}} = \frac{T _{2}}{T _{1}}$
$\Rightarrow \frac{2 E _{1}}{E _{1}} = \frac{T _{2}}{( 20 + 273 )}$
$\Rightarrow T_{2} = 293 \times 2 = 586 K = 31 3^{\circ} C$

Q. At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 20∘C ?

40∘C

80∘C

313∘C

586∘C