Expansion process in a closed system

In a closed system, the expansion process refers to the change in volume that occurs when the system undergoes a physical change, such as heating or cooling. This expansion may result in the performance of work by the system on its surroundings or by the surroundings on the system. The work done is directly related to the value of the expansion index (n) and can be determined using the equation:

W = P * (V2 - V1) / (1 - n)

Where:
W = work done
P = pressure
V2 = final volume
V1 = initial volume
n = expansion index

Influence of expansion index on work done

The expansion index (n) indicates the type of expansion process that occurs. There are three cases to consider:

1. Isothermal expansion (n = 1):
In an isothermal expansion, the temperature of the system remains constant throughout the process. As a result, the work done during an isothermal expansion is given by:

W = P * V * ln(V2/V1)

In this case, the value of n is equal to 1, and as the natural logarithm of the volume ratio increases, the work done also increases. Therefore, the work given out during an isothermal expansion increases when the value of n increases.

2. Adiabatic expansion (n > 1):
In an adiabatic expansion, there is no heat exchange between the system and its surroundings. The work done during an adiabatic expansion is given by:

W = (P2 * V2 - P1 * V1) / (n - 1)

In this case, the value of n is greater than 1. As n increases, the denominator of the equation decreases, resulting in a larger value for the work done. Therefore, the work given out during an adiabatic expansion also increases when the value of n increases.

3. Isobaric expansion (n = 0):
In an isobaric expansion, the pressure of the system remains constant throughout the process. The work done during an isobaric expansion is given by:

W = P * (V2 - V1)

In this case, the value of n is equal to 0, and the work done is directly proportional to the change in volume. Therefore, the work given out during an isobaric expansion is independent of the value of n.

Conclusion

In a closed system, the work given out during the expansion process will increase when the value of the expansion index (n) increases. This is true for both isothermal and adiabatic expansions. However, in the case of isobaric expansions, the work done is independent of the value of n.

W = (p1v1- p2v2)/(n-1);
since , work done is negative in expansion.
hence , n will increase, negative value of work will decrease.
hence , actual value of work will increase.