Thermodynamics Terms

Step 1: First Law of Thermodynamics.
The first law of thermodynamics states that energy cannot be created or destroyed; it can only be transferred or converted from one form to another. This is a direct application of the law of conservation of energy.
Step 2: Analyzing the options.

- (1) momentum: The first law of thermodynamics does not deal with momentum.
- (2) energy: Correct. The first law deals directly with the conservation of energy.
- (3) mass: This is a concept addressed in mass-energy equivalence, but not directly in the first law of thermodynamics.
- (4) velocity: The first law does not deal with velocity.

Step 3: Conclusion.
The first law of thermodynamics is consistent with the law of conservation of energy, corresponding to option (2).

Step 1: Use the adiabatic condition.
For an adiabatic process, the relation between pressure and temperature is given by: where is the adiabatic index, and are the initial and final temperatures, and and are the initial and final pressures.
Step 2: Apply the given condition.
It is given that the final temperature is twice the initial temperature : Substitute into the adiabatic equation: Thus, the ratio of final pressure to initial pressure is: For a mono-atomic ideal gas, , so: