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Heat and Thermodynamics question

2023 · 8 Apr · Shift 2 · Q54
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Heat and Thermodynamics question

2023 · 8 Apr · Shift 2 · Q54

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27∘C27^{\circ} \mathrm{C}27∘C is
  1. A
    627∘C627^{\circ} \mathrm{C}627∘C
  2. B
    927∘C927^{\circ} \mathrm{C}927∘C
  3. C
    327∘C327^{\circ} \mathrm{C}327∘C
  4. D
    1227∘C1227^{\circ} \mathrm{C}1227∘C
View written solutionFree

Correct answer: C

  1. Relation between kinetic energy and temperature

For an ideal gas, the average kinetic energy of a molecule is directly proportional to the absolute temperature:

Ek∝TE_k \propto TEk​∝T

So, if the kinetic energy becomes double, then the absolute temperature must also become double.

  1. Convert the initial temperature into Kelvin

Given initial temperature:

27∘C=27+273=300 K27^\circ \mathrm{C} = 27 + 273 = 300\,\mathrm{K}27∘C=27+273=300K

  1. Double the absolute temperature

If kinetic energy doubles,

T2=2T1=2×300=600 KT_2 = 2T_1 = 2 \times 300 = 600\,\mathrm{K}T2​=2T1​=2×300=600K

  1. Convert back to Celsius

T2=600−273=327∘CT_2 = 600 - 273 = 327^\circ \mathrm{C}T2​=600−273=327∘C

  1. Match with the options

327∘C327^\circ \mathrm{C}327∘C corresponds to Option C.

Final Answer

The required temperature is:

327∘C\boxed{327^\circ \mathrm{C}}327∘C​

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