Question

If a gas expands at constant temperature, it indicates that:
(a) Kinetic energy of the molecules decreases
(b) pressure of the gas increases
(c) kinetic energy of the molecules remains same
(d) number of the molecules of gas increases

Answer 1

Hint: Gas is a state of matter. There are various laws to explain the behaviour of gases under different conditions of temperature, pressure and volume such as Boyle’s Law, Charles Law, Gay-Lussac’s law and Avogadro Law.

Complete step by step solution:
We know that the ideal gas equation is \[PV=nRT\].
In the P is the pressure, V is the volume of the gas, n is the number of moles of gas involved. R is Rydberg constant and T is the temperature.
From this equation, we get to know that for a given mass of gas, at constant temperature, the pressure is inversely proportional to volume. So, at constant temperature, when the gas expands, the pressure decreases.
For average kinetic energy, the expression is\[\dfrac{3}{2}RT\], where R is the Reydberg Constant and T is the temperature. Therefore, at a constant temperature, the kinetic energy will also be the same.
\[KE=\dfrac{3}{2}RT\]
\[KE\propto T\]
Therefore, when gas expands at a constant temperature, pressure decreases as well as kinetic energy of the molecules will remain the same. Hence, correct options are (b) and (c).

Additional Information:
Ideal gas law describes the behaviour of an ideal gas. Actually ideal gas is a hypothetical gas whose behaviour can be explained by the ideal gas law and the kinetic molecular theory of gases. We know that standard temperature and pressure (STP) is at 298K and 1atm and standard volume is 1 mol of an ideal gas at STP is 22.4L. All empirical gas relationships are special cases of the ideal gas in which any two of the parameters, out of the four, is held constant. Ideal gas laws give values of the fourth quantity of the gas, by keeping any two parameters constant. It is also used to find the density of a gas if its molar mass is known and vice versa.

Note: In this question two options are correct. The relation between the temperature, pressure, kinetic energy of the molecules should be known in order to find the correct answers. Boyle’s Law is based on the relationship between pressure and volume at constant temperature. Charles Law is the temperature-volume law where the pressure is kept constant. Gay-Lussac’s law involved the temperature-pressure law where volume is kep constant and Avogadro Law gives the relationship between the volume and the amoun provided that the temperature and pressure is constant.