`50 L` of a certain liquid is confined in a piston system at the external pressure `100 atm`. This pressure is suddenly released and liquid is expanded against the constant atmospheric pressure, volume of the liquid increases by `1 L` and the final pressure on the liquid is `10 atm`. Find the workdone.

Options

A. `1 L. atm`
B. `5 L.atm`
C. `5000 L. atm`
D. `50 L.atm`

Answer

To solve the problem of work done during the expansion of the liquid in a piston system, we will follow these steps:

### Step 1: Identify the initial and final conditions
- Initial volume (V1) = 50 L
- Final volume (V2) = V1 + 1 L = 50 L + 1 L = 51 L
- External pressure (P_ext) = 100 atm (before release)
- Final pressure (P_final) = 10 atm (after expansion)

### Step 2: Determine the change in volume (ΔV)
- ΔV = V2 - V1
- ΔV = 51 L - 50 L = 1 L

### Step 3: Calculate the work done (W)
Since the expansion occurs against a constant atmospheric pressure after the initial pressure is released, we use the formula for work done during expansion at constant pressure:
\[ W = P \Delta V \]
Here, we will use the final pressure (10 atm) for the calculation of work done because the liquid expands against this pressure.

### Step 4: Substitute the values into the work formula
- Work done (W) = P_final × ΔV
- W = 10 atm × 1 L

### Step 5: Convert the units if necessary
1 L atm is equivalent to 101.325 J (joules), but since the question does not specify a need for conversion, we can keep the answer in L atm.
- W = 10 L atm

### Final Answer
The work done during the expansion of the liquid is **10 L atm**.

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