MULTIPLE ANSWER QUESTION

AN IDEAL MONOATOMIC GAS AT NTP IS ENCLOSED IN AN ADIABATIC VERTICAL CYLINDER BETWEEN TWO LIGHT MOVABLE PISTONS (ONE UP AND ONE DOWN). SPRING WITH FORCE CONSTANT K IS CONNECTED TO THE UPPER PISTON AND IS IN A RELAXED STATE INITIALLY. THE LOWER PISTON IS MOVED UP BY A DISTANCE OF H/2, H BEING THE INITIAL LENGTH OF GAS COLUMN. IT IS OBSERED THAT THE UPPER PISTON MOVES UP BY H/16.

Q. WHEN THE LOWER PISTON IS MOVED UPWARDS BY H/2,THE COMPRESSION

A) LEADS TO COOLING

B) TAKES PLACE ISOTHERMALLY

C) TAKES PLACE ADIABATICALLY

D) LEADS TO HEATING

To tackle this question, we need to consider the properties of an ideal monatomic gas and the conditions under which the gas is being compressed. The scenario describes an adiabatic process, which means that there is no heat exchange with the surroundings. Let's break down the implications of moving the lower piston and how it affects the gas.

Understanding the Process

When the lower piston is moved upwards by a distance of H/2, the volume of the gas decreases. Since the system is adiabatic, the gas does not exchange heat with its environment. This is crucial because it determines how the gas behaves during compression.

Key Concepts of Adiabatic Processes

• Adiabatic Compression: In an adiabatic process, when a gas is compressed, its internal energy increases, leading to a rise in temperature. This is due to the work done on the gas by the pistons.
• Ideal Gas Law: The relationship between pressure, volume, and temperature is governed by the ideal gas law, which states that PV = nRT. In an adiabatic process, the relationship is modified to account for the lack of heat exchange.
• Work Done on the Gas: The work done on the gas during compression results in an increase in its internal energy, which translates to an increase in temperature.

Analyzing the Options

Now, let's evaluate the options provided in the question:

• A) Leads to cooling: This option is incorrect. In an adiabatic compression, the gas heats up rather than cools down.
• B) Takes place isothermally: This option is also incorrect. Isothermal processes occur at constant temperature, which is not the case here since the process is adiabatic.
• C) Takes place adiabatically: This option is correct. The problem states that the gas is enclosed in an adiabatic cylinder, meaning that the compression occurs without heat exchange.
• D) Leads to heating: This option is correct as well. The compression of the gas leads to an increase in temperature due to the work done on it.

Conclusion

In summary, when the lower piston is moved upwards by H/2 in an adiabatic process, the correct answers are C) Takes place adiabatically and D) Leads to heating. The gas experiences an increase in temperature due to the work done on it during the compression, consistent with the principles of thermodynamics governing adiabatic processes.