Question

At constant volume, for a fixed number of moles of a gas, the pressure of the gas increases with the rise in temperature due to:
A. Increase in average molecular speed
B. Increase in the rate of collisions among the molecules
C. Increase in the molecular attraction
D. Decrease in the mean free path

Answer 1

Hint: Pressure is defined as a force exerted by a substance on an area of one unit on another substance. The formula of pressure is force/Area. Gaseous molecules exert pressure on the walls of the vessel where it is present. For example, on inflating a balloon the gaseous molecules inside the balloon exert pressure due to which the balloon expands.

Complete Step by Step Solution:
Let's understand what happens when the temperature is increased at constant volume. We know that pressure is equal to the momentum change per unit time in per unit area. When the volume is kept constant, for a fixed quantity of gas, the increase of pressure occurs on increasing temperature because of the increase of the average speed of the molecules. This results in the momentum change during the collision of particles with the walls.

Therefore, when the average speed of molecules increases at constant volume, the increase of the pressure of gaseous molecules takes place.
Hence, option A is right.

Note: The mathematical expression for an ideal gas is PV = nRT, where P, V, R, n and T stand for pressure, volume, Gas constant, mole of electrons and temperature respectively. This equation also shows that the relation between pressure and temperature is directly proportional.