Which of the following expression represent the first law of thermodynamics?

Options

A. `DeltaE=-q+W`
B. `Delta=q+W`
C. `DeltaE=q+W`
D. `DeltaE=-q-W`

Answer

To determine which expression represents the first law of thermodynamics, we need to understand the components involved in the law itself. The first law of thermodynamics can be expressed in terms of internal energy (U), heat (Q), and work (W).

### Step-by-Step Solution:

1. **Understanding the First Law of Thermodynamics**:
The first law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). This can be mathematically expressed as:
\[ \Delta U = Q - W \]

2. **Identifying the Components**:
- **ΔU**: Change in internal energy of the system.
- **Q**: Heat added to the system.
- **W**: Work done by the system.

3. **Rearranging the Equation**:
The equation can also be rearranged to express Q in terms of ΔU and W:
\[ Q = \Delta U + W \]
This shows that the heat added to the system is equal to the change in internal energy plus the work done by the system.

4. **Considering Alternative Forms**:
Sometimes, the work done on the system is considered instead of the work done by the system. In that case, the equation can be expressed as:
\[ \Delta U = Q + W_{on} \]
where \(W_{on}\) is the work done on the system.

5. **Conclusion**:
The correct expression that represents the first law of thermodynamics is:
\[ \Delta U = Q - W \]