Thermodynamics

Step 1: Use the First Law of Thermodynamics.
where:
is the change in internal energy,
is the heat added to the system,
is the work done by the system.
Step 2: Use the condition for an adiabatic process.
In an adiabatic process, no heat is exchanged: Thus, the equation becomes: Step 3: Substitute the given value.
Work done by the gas is , so: Therefore, the internal energy of the gas decreases by 500 J.

This is a direct application of the ideal gas law:
If pressure and number of moles are constant, then the equation simplifies to:
This means that volume is directly proportional to temperature (in Kelvin).
So, if the temperature is doubled:
Hence, the volume also doubles.
Let’s say the initial temperature is , and volume is . After doubling the temperature to , the volume becomes .