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

Options

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

Answer

To solve the question based on the first law of thermodynamics, we need to analyze the four processes mentioned: isothermal, isochoric, adiabatic, and cyclic. We will apply the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added to the system (Q) plus the work done on the system (W). The equation can be expressed as:

\[ \Delta U = Q + W \]

### Step-by-Step Solution:

1. **Understand the First Law of Thermodynamics**:
- The first law states that energy cannot be created or destroyed, only transformed. The equation is ΔU = Q + W.

2. **Analyze the Isothermal Process**:
- In an isothermal process, the temperature remains constant (ΔT = 0), which implies that ΔU = 0.
- Therefore, from the first law:
\[ 0 = Q + W \implies Q = -W \]
- This means that the heat added to the system is equal to the negative of the work done by the system. This option does not match any of the provided options.

3. **Analyze the Isochoric Process**:
- In an isochoric process, the volume remains constant (ΔV = 0). Hence, no work is done (W = 0).
- Thus, from the first law:
\[ \Delta U = Q \implies Q = \Delta U \]
- If the option states that heat is negative, then this option is incorrect.

4. **Analyze the Adiabatic Process**:
- In an adiabatic process, there is no heat exchange (Q = 0).
- Therefore, from the first law:
\[ \Delta U = W \]
- If the option states that ΔU is negative, then this option is also incorrect.

5. **Analyze the Cyclic Process**:
- In a cyclic process, the system returns to its initial state, so ΔU = 0.
- Therefore, from the first law:
\[ 0 = Q + W \implies Q = -W \]
- This means that the heat added to the system is equal to the negative of the work done by the system, which matches our derived equation.

6. **Conclusion**:
- The correct option based on the analysis is the cyclic process, where ΔU = 0 and Q = -W.

### Final Answer:
The correct statement based on the first law of thermodynamics is related to the cyclic process, where ΔU = 0, leading to Q = -W.

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