Given information:
Initial temperature (T1) = 25 degrees Celsius = 298 Kelvin
Initial pressure (P1) = 5 atmospheres
Final volume (V2) = 2 times initial volume (V1)

Adiabatic process:
An adiabatic process occurs when there is no heat exchange between the system and its surroundings. This means that the change in internal energy of the gas is solely due to work done on or by the gas.

Adiabatic expansion:
In an adiabatic expansion, the gas does work on the surroundings by pushing against a constant external pressure. This leads to a decrease in the internal energy and temperature of the gas.

Specific heat capacity at constant volume:
The specific heat capacity at constant volume (Cv) is the amount of heat required to raise the temperature of a unit mass of a substance by 1 degree Celsius while keeping the volume constant. For an ideal gas, Cv is given by Cv = (5/2)R, where R is the ideal gas constant.

Calculating the final temperature (T2):
To find the final temperature (T2) after the expansion, we can use the adiabatic expansion formula:

(P1 * V1^(γ-1)) / T1 = (P2 * V2^(γ-1)) / T2

Where γ is the ratio of specific heat capacities (Cp/Cv) and is equal to 5/3 for an ideal gas.

Calculating the initial volume (V1):
To find the initial volume (V1), we can use the ideal gas law equation: PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

V1 = (nRT1) / P1

Solution:
1. Convert the initial temperature to Kelvin: T1 = 25 degrees Celsius + 273.15 = 298 Kelvin
2. Calculate the initial volume using the ideal gas law equation: V1 = (nRT1) / P1
3. Since the number of moles (n) is not given, we can assume it to be 1 for simplicity.
V1 = (1 * R * 298) / 5 = 59.6R
4. Calculate the final pressure (P2) using the given constant pressure: P2 = 1 atmosphere
5. Calculate the final volume (V2) by doubling the initial volume: V2 = 2 * V1 = 2 * 59.6R = 119.2R
6. Substitute the values into the adiabatic expansion formula:
(5 * 59.6R^(5/3 - 1)) / 298 = (1 * 119.2R^(5/3 - 1)) / T2
7. Simplify the equation:
(5 * 59.6R^(2/3)) / 298 = (1 * 119.2R^(2/3)) / T2
8. Cross multiply and solve for T2:
(5 * 119.2R^(2/3)) = (1