Heat and Thermodynamics 4 Question 34
36. From the following statements concerning ideal gas at any given temperature $T$, select the correct one (s). (1995, 2M)
(a) The coefficient of volume expansion at constant pressure is the same for all ideal gases
(b) The average translational kinetic energy per molecule of oxygen gas is $3 k T, k$ being Boltzmann constant
(c) The mean-free path of molecules increases with decrease in the pressure
(d) In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different
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Solution:
- For one mole of an ideal gas
$$ p V=R T $$
The coefficient of volume expansion at constant pressure is given by,
$$ \left(\frac{\Delta V}{\Delta T}\right) _p=\frac{R}{p}=\text { constant } $$
[option (a)]
The average translational kinetic energy per molecule is (3/2) $k T$ and not $3 k T$. With decrease of pressure, volume of the gas increases so its mean free path. [option (c)] The average translational kinetic energy of the molecules is independent of their nature, so each component of the gaseous mixture will have the same value of average translational kinetic energy.
