Question

The following statements are given : 
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced 
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature 
(3) The average kinetic energy of a gas molecule decreases with increases in volume 
(4) Pressure of a gas increases with increase in temperature at constant pressure 
(5) The volume of gas decreases with increase in temperature 
Choose the correct answer from the options given below :

• A. (1) and (4) only
• B. (1), (2) and (4) only
• C. (2) and (4) only
• D. (1), (2) and (5) only

Answer 1

The Correct Option is A

To determine the correct statements regarding the average kinetic energy of a gas molecule, let's analyze each statement one by one:

1. The average kinetic energy of a gas molecule decreases when the temperature is reduced: According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. Thus, when the temperature decreases, the average kinetic energy also decreases. This statement is true.
2. The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature: At constant temperature, the average kinetic energy is solely dependent on the temperature of the gas, not on the pressure. Hence, this statement is false.
3. The average kinetic energy of a gas molecule decreases with increases in volume: Similar to pressure, the volume doesn't directly affect the average kinetic energy of gas molecules. It is again the temperature that plays the pivotal role. Therefore, this statement is false.
4. Pressure of a gas increases with increase in temperature at constant pressure: This seems to be an erroneous statement. It should be interpreted correctly as the pressure of a gas increases with an increase in temperature at constant volume as per Gay-Lussac’s law. Since the statement conditions are incorrectly set, it can be considered false when read literally, but the context might suggest another interpretation.
5. The volume of gas decreases with increase in temperature: According to Charles' Law, at constant pressure, the volume of a gas increases with an increase in temperature. Therefore, this statement is false.

Upon careful evaluation of these statements, only statement (1) is entirely correct based on the fundamental principles of the kinetic theory of gases. Considering the statement about pressure (4), interpreting it correctly based on gas laws, might lead to the literal confusion where it could mean at constant volume, the pressure increases with temperature.

Therefore, the correct answer based on logical interpretation and provided options is: (1) and (4) only.