Question

At constant volume, temperature is increased then
A. collision on walls will be less
B. number of collisions per unit time will increase
C. collisions will be in straight lines
D. collisions will not change

Answer 1

Hint: As a first step, you could recall the Ideal gas equation and thus find the proportionality relation of temperature with pressure at constant volume. Now you could recall the relation of pressure with the number of collisions. Thus, you could find what happens to the number of collisions when the temperature is increased.

Formula used:
Ideal gas equation,
$PV=nRT$

Complete step-by-step answer:
In the question, we are given a number of options and we are asked to find which among happens when the temperature of a gas is increased at constant volume.
In order to answer this, let us recall the ideal gas equation which is given by,
$PV=nRT$
Where, P is the pressure of the gas, V is the volume, n is the number of moles of gas present, R is the ideal gas constant and T is the temperature.
We already know that R is a constant and in addition we are given that the volume is constant and so will be the number of moles. Hence, we find from the ideal gas equation that,
$P\propto T$
As P is found to be directly proportional to temperature, when the temperature is increased, the pressure will also be increased. But, we know that, the pressure of a gas is directly proportional to the number of collisions. So, an increase in temperature results in an increase of pressure and hence the increase in number of collisions.
Therefore, we found that, at constant volume when the temperature is increased the number of collisions per unit time will increase.

So, the correct answer is “Option B”.

Note: Ideal gas equation is actually the equation of state for a hypothetical ideal gas. It is actually the combination of various laws, namely, Boyle’s law, Charles’s law, Gay-Lussac’s law and Avogadro’s law. This can also be derived from the kinetic theory of gases. It is also known to be a very good approximation of the behavior of many gases.