At which of the following temperatures would molecules have twicethe average kin

Question

At which of the following temperatures would molecules have twicethe average kinetic energy they have at room temperature, 20oC?

A)40 oC
B)68 oC
C)80 oC
D)313 oC
E)586 oC Hint: The kinetic energy is proportional to the absolutetemperature. The molecules have twice the average kineticenergy if the absolute temperature doubles.
20oC = 293K 2*293K = 586K = (586-273)oC.

A)40 oC
B)68 oC
C)80 oC
D)313 oC
E)586 oC Hint: The kinetic energy is proportional to the absolutetemperature. The molecules have twice the average kineticenergy if the absolute temperature doubles.
20oC = 293K 2*293K = 586K = (586-273)oC. Hint: The kinetic energy is proportional to the absolutetemperature. The molecules have twice the average kineticenergy if the absolute temperature doubles.
20oC = 293K 2*293K = 586K = (586-273)oC.

Explanation / Answer

We know that : .              K.E of gas is :  (3/2) kB T .              Hence Kinetic energy is directly proportional to absolutetemperature . Given : .              Initial temperature (T1)   = 20oC   = 20 + 273 = 293 K . If K.E doubles , Temperature also boubles . .                 T2 = 2 * 293 K =   586 K .      In degree centigrade:   T2   = 586 K   - 273   =   313oC . Hope this helps u! .

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