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Question

What is the average translational kinetic energy of molecules in an ideal gas at 37°C?


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Solution

Translational kinetic energy

  • The energy necessary to accelerate a rigid body from rest to a certain velocity is known as the object's translational kinetic energy.
  • Motion from one point to another that follows a straight line is referred to as translational motion.

Ideal gas translational kinetic energy

  • A pure material has more energy in its gaseous state than in its liquid state, which has more energy than in its solid-state.
  • When particles are in a gaseous form, their kinetic energy is at its maximum.
  • There are no attraction forces between the gas molecules in an ideal gas, and the molecules themselves are neither rotating nor vibrating.
  • An ideal gas's temperature affects the kinetic energy of its translational motion.

Formula of average translational kinetic energy

  • The average translational kinetic energy is as follows:

E=32KB×T

  • E=average kinetic energy per molecule of gas.
  • kB=Boltzmann's constant.
  • T=Temperature

Convert degrees Celsius into Kelvin

  • The conversion of degrees Celsius into Kelvin is done as follows:

TK=T°C+273

  • Convert 37°C into Kelvin as follows:

TK=T°C+273=37+273=310K

Calculate average translational kinetic energy

  • The average translational kinetic energy of molecules in an ideal gas is as follows:

E=32KB×T=32×1.38×1023JK-1×310K=1283.4×1023J2=641.7×1023J

  • The average translational kinetic energy of molecules in an ideal gas is 641.7×1023J.

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