`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 calculating the work done when a liquid expands in a piston system, we can follow these steps:

### Step 1: Identify the Initial and Final Conditions
- Initial volume (V_initial) = 50 L
- Final volume (V_final) = 51 L (since the volume increases by 1 L)
- External pressure (P_external) = 100 atm
- Final pressure (P_final) = 10 atm

### Step 2: Calculate the Change in Volume
The change in volume (ΔV) can be calculated as:
\[ \Delta V = V_{final} - V_{initial} = 51 \, \text{L} - 50 \, \text{L} = 1 \, \text{L} \]

### Step 3: Convert Volume Change to Appropriate Units
Since work is often expressed in Joules, we need to convert the volume change from liters to cubic meters or use the appropriate conversion factor.
1 L atm is approximately equal to 101.3 Joules. Therefore:
\[ \Delta V = 1 \, \text{L} = 1 \, \text{L} \times 101.3 \, \text{J/L atm} = 101.3 \, \text{J} \]

### Step 4: Calculate Work Done
The work done (W) during expansion against a constant external pressure can be calculated using the formula:
\[ W = P_{external} \times \Delta V \]
Substituting the values:
\[ W = 100 \, \text{atm} \times 1 \, \text{L} \]
Now converting this to Joules:
\[ W = 100 \, \text{atm} \times 101.3 \, \text{J/L atm} = 10130 \, \text{J} \]

### Step 5: Final Answer
Thus, the work done during the expansion is:
\[ W = 10130 \, \text{J} \]