At constant volume, for a fixed number of moles of a gas the pressure of the gas increases with rise of temperature due to:a)Increase in average molecular speed b)Increase rate of collisions amongst moleculesc)Increase in molecular attraction d)Decrease in mean freed pathCorrect answer is option 'A'. Can you explain this answer?

Question

At constant volume, for a fixed number of moles of a gas the pressure of the gas increases with rise of temperature due to:a)Increase in average molecular speed     b)Increase rate of collisions amongst moleculesc)Increase in molecular attraction         d)Decrease in mean freed pathCorrect answer is option 'A'. Can you explain this answer?

Answer

Explanation:

When the temperature of a gas is increased, the kinetic energy of the gas molecules also increases. This increase in kinetic energy leads to an increase in the average molecular speed of the gas molecules. Due to this, the pressure of the gas increases at a constant volume.

The relationship between pressure and temperature can be explained by the kinetic theory of gases, which states that the pressure of a gas is directly proportional to the average kinetic energy of its molecules. The higher the temperature of the gas, the higher the average kinetic energy of its molecules and hence the higher the pressure.

At a constant volume, the rate of collisions amongst the gas molecules also increases with an increase in temperature. This is because the gas molecules move faster at higher temperatures and collide with each other more frequently. However, the increase in pressure is primarily due to the increase in average molecular speed.

The other options given in the question are not correct. An increase in molecular attraction would lead to a decrease in pressure, not an increase. A decrease in mean free path would also lead to a decrease in pressure. Therefore, option A is the correct answer.

Conclusion:

In conclusion, the pressure of a gas increases at a constant volume when the temperature of the gas is increased. This increase in pressure is due to an increase in the average molecular speed of the gas molecules, which in turn is due to an increase in the kinetic energy of the gas molecules.

Answer

As temperature increases, Kinetic energy of molecule increases. This increases the velocity of molecules. Thus now in particular time more molecules can hit the wall of container , which increases pressure.
Mathematically, it can be given by Kinetic gas theoryi.e. P*V =( m*N*v^2) / 3 Where N = no.of molecules ; v= velocity of molecule ; m = Mass of one molecule ; P = pressure ; V = volume
When gas, moles, volume are fixed, V,N, m are constant So, P ∝ v Also v ∝ T Now as Temperature increases , v increases and thus P increases.

Answer

I think that when pressue increases average molecular speed also increases.

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