The dependence of Gibbs free energy on pressure for an isothermal process of an ideal gas is given by

Options

A. `triangleG_(r)=nRT ln P_(2)/P_(1)`
B. `triangleG_(T)=nRT ln V_(2)'/V_(1)`
C. `triangleG_(T)=nRT ln P_(1)/P_(2)`
D. `triangleG_(T)=nRT log V_(1)/V_(2)`

Answer

To find the dependence of Gibbs free energy (G) on pressure (P) for an isothermal process of an ideal gas, we can follow these steps:

### Step 1: Understand the Isothermal Process
An isothermal process is one in which the temperature (T) remains constant. For an ideal gas undergoing an isothermal process, the internal energy change (ΔU) is zero since it only depends on temperature.

### Step 2: Define Gibbs Free Energy
Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The formula for Gibbs free energy is:
\[ G = H - TS \]
where H is the enthalpy, T is the temperature, and S is the entropy.

### Step 3: Relate Gibbs Free Energy to Pressure
For an ideal gas, the change in Gibbs free energy (ΔG) with respect to pressure can be expressed as:
\[ \Delta G = nRT \ln \left( \frac{P_2}{P_1} \right) \]
where:
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature
- \( P_1 \) = initial pressure
- \( P_2 \) = final pressure

### Step 4: Conclusion
Thus, the dependence of Gibbs free energy on pressure for an isothermal process of an ideal gas is given by the equation:
\[ G(P) = G(P_1) + nRT \ln \left( \frac{P}{P_1} \right) \]
This indicates how Gibbs free energy changes as the pressure changes in an isothermal process.

### Final Answer
The dependence of Gibbs free energy on pressure for an isothermal process of an ideal gas is:
\[ \Delta G = nRT \ln \left( \frac{P_2}{P_1} \right) \]