Understanding Thermodynamic Processes in a Closed System

In thermodynamics, a closed system is one that can exchange energy (heat and work) with its surroundings but not matter. The behavior of a closed system undergoing different processes is often described by the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:

\( \Delta U = Q - W \)

Where:

• \( \Delta U \) is the change in internal energy of the system.
• \( Q \) is the heat added to the system.
• \( W \) is the work done by the system.

The question asks to identify specific thermodynamic processes in a closed system where Heat, Work done, and Internal Energy change are zero, respectively. Let's analyze each condition.

Identifying Processes with Zero Heat, Work, or Internal Energy

1. Heat Transfer is Zero (\(Q = 0\))

A process in which no heat is transferred into or out of the system is called an adiabatic process. In an adiabatic process, \(Q = 0\). According to the First Law, \( \Delta U = -W \). This means any work done by the system comes from a decrease in internal energy, and any work done on the system increases its internal energy. Examples include rapid expansion or compression of a gas.

2. Work Done is Zero (\(W = 0\))

Work done by a closed system (like a gas expanding against a piston) is typically boundary work, given by \( W = \int P \, dV \), where \(P\) is the pressure and \(dV\) is the change in volume. For the work done \(W\) to be zero in a process where pressure is generally non-zero, the change in volume (\(dV\)) must be zero throughout the process. A process that occurs at constant volume (\(V = \text{constant}\)) is called an isochoric process. In an isochoric process, \(W = 0\). The First Law becomes \( \Delta U = Q \), meaning any heat added to the system directly increases its internal energy, and heat removed decreases its internal energy.

3. Internal Energy Change is Zero (\(\Delta U = 0\))

For an ideal gas, internal energy (\(U\)) depends only on temperature (\(T\)). The change in internal energy is given by \( \Delta U = nC_v \Delta T \), where \(n\) is the number of moles and \(C_v\) is the molar heat capacity at constant volume. For the change in internal energy to be zero (\(\Delta U = 0\)), the change in temperature (\(\Delta T\)) must be zero. A process that occurs at constant temperature (\(T = \text{constant}\)) is called an isothermal process. In an isothermal process for an ideal gas, \( \Delta U = 0 \). According to the First Law, \( 0 = Q - W \), which implies \( Q = W \). This means any heat added to the system is completely converted into work done by the system, and any work done on the system is dissipated as heat removed from the system, keeping the temperature constant.

Summary of Processes and Zero Quantities

To summarize the findings:

Matching with the Question Conditions

The question asks for the processes where Heat, Work done, and Internal Energy are zero, in that specific order. Based on our analysis:

• When Heat is zero, the process is Adiabatic.
• When Work done is zero, the process is Isochoric.
• When Internal energy is zero, the process is Isothermal.

Therefore, the required sequence of processes is Adiabatic, Isochoric, and Isothermal.

Conclusion

For a closed system, the process where Heat is zero is an Adiabatic process. The process where Work done is zero is an Isochoric process. The process where Internal Energy change is zero (specifically for an ideal gas) is an Isothermal process. Thus, the sequence Adiabatic, Isochoric, Isothermal correctly identifies the processes where the respective quantities are zero.