Thermodynamic Analysis of Isothermal Expansion

The question describes an isothermal expansion of an ideal gas where the net heat supplied equals the net work done.

We need to check the validity of this process using the laws of thermodynamics.

First Law of Thermodynamics

The first law of thermodynamics states that for a closed system:

$ \Delta U = Q_{net} - W_{net} $

Where:

• $ \Delta U $ is the change in internal energy.
• $ Q_{net} $ is the net heat supplied to the system.
• $ W_{net} $ is the net work done by the system.

Applying Conditions to the First Law

For an ideal gas undergoing an isothermal process, the temperature remains constant ($ \Delta T = 0 $).

Since the internal energy ($U$) of an ideal gas depends only on temperature, the change in internal energy is zero:

$ \Delta U = 0 $

Substituting $ \Delta U = 0 $ into the first law equation gives:

$ 0 = Q_{net} - W_{net} $

This simplifies to:

$ Q_{net} = W_{net} $

The condition given in the question ($Q_{net} = W_{net}$) is therefore consistent with the first law of thermodynamics for an isothermal expansion of an ideal gas.

Second Law Consideration

The second law of thermodynamics places restrictions on the direction of heat flow and the efficiency of converting heat into work. However, the scenario described ($Q_{net} = W_{net}$) for a single isothermal expansion step does not inherently violate the second law. It simply means all the heat added during the expansion is converted into work, which is consistent with $ \Delta U = 0 $.

Conclusion

The process described satisfies the first law of thermodynamics for an isothermal expansion of an ideal gas and does not violate the second law.

Therefore, the statement "The process is possible" is correct.