Manipal MET2019ChemistryStates of Matter
The kinetic energy of a gas molecule is _____ temperature
Options
- Aindependent of
- Bdirectly proportional to
- Cinversely proportional to
- Ddirectly proportional to square root of
Correct answer
B. directly proportional to
Step-by-step solution
The kinetic energy of a gas molecule is directly proportional to absolute temperature. According to kinetic theory of gases, the pressure P exerted by a gas is given by p= 1 3 M u^2 V or p V= 1 3 M u^2 According to gas equation p V=R T 1 3 M u^2=R T or 1 M u^2 3 N = R T N We know that R N =KK= Boltzmann constant or 1 2 M u^2= 3 2 K T But 1 2 M u^2 is average kinetic energy per molecule of the gas. Average K.E. = 3 2 K T K.E. T Thus average kinetic energy of one mole of any gas is directly proportional to its absolu