Laws Of Thermodynamics

To solve the problem, we need to find the total change in enthalpy for the transformation of state in the sequence .

1. Given Data:
We are given moles of an ideal monoatomic gas.
Also, and .

2. Relationship Between Enthalpy and Temperature:
For an ideal gas, enthalpy is a function of temperature only. The differential change in enthalpy is given by:


where is the molar heat capacity at constant pressure.

3. Heat Capacities for a Monoatomic Gas:
For a monoatomic gas, we have:

and .

4. Calculating Molar Heat Capacity at Constant Pressure:
The molar heat capacity at constant pressure is:

.

5. Change in Enthalpy Formula:
The change in enthalpy is given by:


or

.

6. Temperatures at States:
The temperature at state is , at state is , and at state is .

7. Change in Enthalpy for Process :
Since the temperature is constant between states and , the change in enthalpy is:

.

8. Change in Enthalpy for Process :
The change in temperature for the process is:

.

9. Calculating the Change in Enthalpy for :
We can now calculate the change in enthalpy for the process as:

.

10. Total Change in Enthalpy:
The total change in enthalpy is the sum of the changes for each process:

.

Final Answer:
The final answer is .