Given:
- Number of moles of gas (n) = 0.2 mol
- Initial volume (V1) = 1 dm^3
- Final volume (V2) = 0.25 dm^3

Assumptions:
- The process is reversible, which implies that the gas is in thermodynamic equilibrium at all times.
- The process is adiabatic, which means that there is no heat exchange between the gas and its surroundings.
- The gas behaves ideally, following the ideal gas law.

Calculating work done (w):
The work done during a reversible adiabatic process can be calculated using the formula:

w = -nRT1 * (V2 - V1) / (γ - 1)

where:
- n is the number of moles of gas
- R is the gas constant
- T1 is the initial temperature of the gas
- V2 is the final volume of the gas
- V1 is the initial volume of the gas
- γ is the heat capacity ratio (Cp/Cv) of the gas

Since the process is adiabatic, there is no heat exchange and the temperature remains constant. Therefore, T1 is equal to the final temperature (T2).

Calculating change in internal energy (ΔU):
The change in internal energy during an adiabatic process can be calculated using the formula:

ΔU = q + w

Since the process is adiabatic, there is no heat exchange (q = 0). Therefore, the change in internal energy (ΔU) is equal to the work done (w).

Calculating change in enthalpy (ΔH):
The change in enthalpy during an adiabatic process can be calculated using the formula:

ΔH = ΔU + ΔPV

where:
- ΔU is the change in internal energy
- ΔP is the change in pressure
- ΔV is the change in volume

Since the process is adiabatic, there is no heat exchange (q = 0) and the change in pressure is related to the change in volume through the equation:

P1 * V1^γ = P2 * V2^γ

where:
- P1 is the initial pressure of the gas
- P2 is the final pressure of the gas

Calculating ΔU and ΔH:

1. Determine the initial and final pressures of the gas using the ideal gas law equation:

P1 * V1 = nRT1
P2 * V2 = nRT2

2. Calculate the work done (w) using the formula mentioned above.

3. Calculate the change in internal energy (ΔU) as the negative value of the work done (w).

4. Calculate the change in pressure (ΔP) using the equation mentioned above.

5. Calculate the change in enthalpy (ΔH) using the formula mentioned above.

Summary:
- To calculate the work done (w), use the formula w = -nRT1 * (V2 - V1) / (γ - 1).
- The change in internal energy (ΔU) for an adiabatic process is equal to the work done (