Thermodynamics And Work Done

To determine the spontaneity of a reaction based on the effect of temperature, we use the Gibbs free energy change equation:

Where:

• is the change in Gibbs free energy.
• is the change in enthalpy.
• is the temperature in Kelvin.
• is the change in entropy.

The spontaneity of the reaction depends on the signs of and :

1. and :
   • Non-spontaneous at any temperature since both terms increase .
2. and :
   • Spontaneous at high temperature because term can outweigh the positive .
3. and :
   • Spontaneous at low temperature because the negative outweighs the negative .
4. and :
   • Spontaneous at any temperature since both terms decrease .

The correct options are (B) and (C) because they correspond to scenarios 2 and 3, respectively, where reactions can be spontaneous depending on the temperature.

The decomposition of to is given by:

1. Given Thermodynamic Data:
- Standard enthalpy change:
- Standard entropy change:
- Temperature:

2. Gibbs Free Energy Equation:
The standard Gibbs free energy change is calculated using:

3. Calculation:
Substituting the given values:

4. Final Result:
The standard free energy change for this reaction at 25°C is .

Final Answer:
The final answer is .

For an isobaric process (a process occurring at constant pressure), the first law of thermodynamics is given by:

Where:
- is the heat added to the system,
- is the change in internal energy,
- is the work done by the system.

For a diatomic gas, the work done in an isobaric process is:

Also, the change in internal energy for a diatomic gas (which behaves like an ideal gas) is given by:

The heat added to the system in an isobaric process is:

From thermodynamics, the relationship between and for an ideal gas is:

For a diatomic ideal gas, and .

Now, we can calculate the ratio of :

Thus, the ratio is:

Simplifying this, we get:

Therefore, the correct ratio is 7:5:2.