Thermodynamics Terms

This is a matching type question where we need to correctly associate thermodynamic processes with their corresponding properties from two lists.

Let's understand the thermodynamic processes provided in List - I:

• Isothermal Process: In an isothermal process, the temperature remains constant. This means that .
• Isobaric Process: In an isobaric process, the pressure remains constant. This means that .
• Adiabatic Process: In an adiabatic process, no heat is exchanged with the surroundings, keeping the heat content constant. This implies .

Now, List - II describes the properties of these processes:

• Pressure Constant: Refers to an isobaric process where pressure does not change.
• Temperature Constant: Implies an isothermal process where the temperature stays constant.
• Volume Constant: This is characteristic of an isochoric process, which is not listed here, so it must relate to another as a distractor.
• Heat Content Constant: This describes an adiabatic process where no heat is exchanged.

By matching List - I with List - II using our knowledge of these processes:

1. (a) Isothermal matches with (ii) Temperature constant.
2. (b) Isobaric matches with (i) Pressure constant.
3. (c) Adiabatic matches with (iv) Heat content is constant.

The correct combinations according to the given lists and the properties involved are:

• (a) Isothermal → (ii) Temperature constant
• (b) Isobaric → (i) Pressure constant
• (c) Adiabatic → (iv) Heat content is constant

Thus, the correct option is .

Step 1: Apply the Ideal Gas Law for an Isochoric Process

For an isochoric process (constant volume), the ideal gas law can be written as: where is the pressure, is the absolute temperature, is the number of moles, is the ideal gas constant, and is the volume.
Since is constant, we can write: Converting Celsius temperature ( ) to Kelvin ( ), we have .
Substituting:

Step 2: Find the Temperature at Point K

Point K represents the point where the pressure is zero. So: Since is not zero, we must have: Solving:

Conclusion: The temperature corresponding to point K is (Option 4).

Given:

For a constant , we have:

So, the volume expansion coefficient is:

Let's denote the temperatures as follows:

• K (highest temperature)
• K (intermediate temperature)
• K (lowest temperature)

The Carnot engine (E) operates between and , so its efficiency is:

$ E_1 T_H T_M E_2 T_M T_C \eta_{12} \eta_1 + \eta_2 \eta_1 \eta_2 0.4228 < 0.4798 \eta_{12} < \eta_1 + \eta_2 (1 - \eta_1)(1 - \eta_2) = 1 - \eta_{12} \eta_1 \eta_2 > 0 \eta_{12} < \eta_1 + \eta_2 \eta_{12} < \eta_1 + \eta_2 $.

The relation between Celsius and Fahrenheit temperatures is given by the linear equation: This is a straight line with a slope of and a y-intercept of 32, meaning that when the Celsius temperature is 0°C, the Fahrenheit temperature is 32°F. Thus, the relationship between Celsius and Fahrenheit is a straight line with a positive slope that does not pass through the origin but intersects the Fahrenheit axis at 32°F. In the provided options, the correct figure is one where the line passes through the origin and has a positive slope, matching the relationship of the Celsius to Fahrenheit scale (but offset by the starting point).
Final Answer: Option (1).

Assertion A: In a central force field, the work done is independent of the path chosen. This statement is true.
Central forces are conservative forces, and the work done by a conservative force depends only on the initial and final positions, not on the path taken.

Reason R: Every force encountered in mechanics does not have an associated potential energy. This statement is also true. Non-conservative forces like friction and air resistance do not have associated potential energies because the work done by these forces depends on the path taken.

Analysis of the Relationship Between A and R:

• The independence of work done on the path depends on the fact that the force is conservative.
• All conservative forces possess an associated potential energy function.
• Since Reason R states that not every force has an associated potential energy, while Assertion A refers specifically to conservative (central) forces which do have potential energy,
• Reason R is not a correct explanation of Assertion A — it makes a general statement about forces, not specifically about central or conservative forces.

Therefore, both A and R are true, but R is NOT the correct explanation of A.

Final Answer:
The final answer is .