Based on the first law of thermodynamics which one of the following is correct?

Options

A. For an isochoric process, `DeltaE=-q`
B. For an adiabatic process, `DeltaE=-w`
C. For an isothermal process, `q=W`
D. For a cyclic process, `q=-w`

Answer

To solve the question based on the first law of thermodynamics, we will analyze the law and its implications for different processes. The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) plus the work done on the system (W). Mathematically, it can be expressed as:

\[ \Delta U = Q + W \]

Where:
- ΔU = Change in internal energy
- Q = Heat added to the system
- W = Work done on the system

### Step-by-Step Solution:

1. **Understanding the First Law of Thermodynamics**:
- The first law of thermodynamics emphasizes the conservation of energy. Energy can neither be created nor destroyed; it can only be transformed from one form to another.

2. **Analyzing Different Processes**:
- **Isochoric Process**: In this process, the volume remains constant (ΔV = 0). Therefore, no work is done (W = 0). The equation simplifies to:
\[ \Delta U = Q + 0 \implies \Delta U = Q \]
Here, the change in internal energy is equal to the heat added to the system.

- **Adiabatic Process**: In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). Thus:
\[ \Delta U = 0 + W \implies \Delta U = W \]
The change in internal energy is equal to the work done on the system.

- **Isothermal Process**: In an isothermal process, the temperature remains constant. For an ideal gas, this means that the internal energy does not change (ΔU = 0). Therefore:
\[ 0 = Q + W \implies Q = -W \]
The heat added to the system is equal to the negative of the work done by the system.

- **Cyclic Process**: In a cyclic process, the system returns to its initial state. Thus, the change in internal energy over one complete cycle is zero (ΔU = 0). Therefore:
\[ 0 = Q + W \implies Q = -W \]
The heat added to the system is equal to the negative of the work done by the system.

3. **Conclusion**:
- Based on the analysis of these processes, we can conclude that the correct statement based on the first law of thermodynamics will depend on the specific process being described.