if work is done by the system then W is

Options

A. (+)ve
B. (-)ve
C. Zero
D. Depends upon the thermodynamic process.

Answer

To solve the question, we need to analyze the relationship between work done by a thermodynamic system and its volume change. Here’s a step-by-step solution:

### Step 1: Understand the concept of work in thermodynamics
In thermodynamics, work (W) done by a system is defined as the product of pressure (P) and the change in volume (ΔV). The formula for work done by the system can be expressed as:
\[ W = P \times \Delta V \]
where \( \Delta V = V_f - V_i \) (final volume minus initial volume).

### Step 2: Identify the condition given in the question
The question states that work is done by the system. This implies that the system is undergoing an expansion process.

### Step 3: Analyze the change in volume
Since the system is expanding, the final volume (V_f) will be greater than the initial volume (V_i). Therefore, we can express this mathematically:
\[ V_f > V_i \]
This leads to:
\[ \Delta V = V_f - V_i > 0 \]

### Step 4: Determine the sign of work done
From the formula for work:
\[ W = P \times \Delta V \]
Since we have established that \( \Delta V > 0 \) (the change in volume is positive), the work done by the system will also be positive, assuming pressure (P) is also positive during the expansion process.

### Conclusion
Thus, if work is done by the system, then:
\[ W > 0 \]
This means that the work done by the system is positive.

---