Calculation of Entropy Change for Expansion of Ideal Gas

Given data:

- Number of moles of gas (n) = 2
- Initial volume of gas (V1) = 2 L
- Final volume of gas (V2) = 20 L
- Temperature of gas (T) = 27°C = 300 K
- Gas constant (R) = 2 cal/mol K

We can use the formula for entropy change (ΔS) for reversible expansion of ideal gas as:

ΔS = nRln(V2/V1)

Substituting the given values, we get:

ΔS = 2 x 2 x ln(20/2) = 9.2 cal/K

Therefore, the entropy change for the given expansion of ideal gas is 9.2 cal/K.

Explanation:

- Entropy change refers to the measure of the degree of disorder or randomness in a system.
- Reversible expansion of ideal gas is a process in which the gas expands slowly and maintains thermal equilibrium with its surroundings at each step. This ensures that the process is quasi-static and reversible, which means that the system can be restored to its original state by reversing the process without leaving any trace on the surroundings.
- The formula for entropy change for reversible expansion of ideal gas is derived from the second law of thermodynamics, which states that the total entropy of a system and its surroundings always increases for irreversible processes and remains constant for reversible processes.
- The formula shows that entropy change depends on the natural logarithm of the ratio of final and initial volumes of the gas, which reflects the expansion of the gas and the corresponding increase in its entropy.
- The unit of entropy change is cal/K, which means that it represents the amount of heat energy absorbed or released by the system per unit temperature change during the expansion process.
- In this case, the entropy change is positive, which means that the gas becomes more disordered or random as it expands, and the surroundings absorb heat energy.