1 cf at liquid of molar volume 100 mL is kept in an adiabatic container under a pressure of 1 bar.The pressure is steeply increased to 100 bar.Under this constant pressure of 100 bar, the volume of the liquid decreases by 1 mL.Calculate `DeltaU` of the process.

Explanation

To calculate the change in internal energy (ΔU) of the process described, we will follow these steps:

### Step 1: Understand the Process
We have 1 mole of liquid with an initial molar volume of 100 mL. The pressure is increased from 1 bar to 100 bar, and under this constant pressure of 100 bar, the volume of the liquid decreases by 1 mL. Since this is an adiabatic process, we know that no heat is exchanged with the surroundings (Q = 0).

**Hint:** Remember that in an adiabatic process, heat transfer (Q) is zero.

### Step 2: Apply the First Law of Thermodynamics
The first law of thermodynamics states:
\[ \Delta U = Q + W \]
Since Q = 0 for an adiabatic process, we have:
\[ \Delta U = W \]

**Hint:** The first law of thermodynamics relates internal energy change to heat and work done.

### Step 3: Calculate the Work Done (W)
For a constant pressure process, the work done on the system can be expressed as:
\[ W = -P \Delta V \]
Where:
- \(P\) is the pressure (in this case, 100 bar)
- \(\Delta V\) is the change in volume (which is -1 mL, since the volume decreases)

Convert the units:
- Pressure: \(100 \text{ bar} = 100 \times 10^5 \text{ Pa}\) (since 1 bar = \(10^5\) Pa)
- Change in volume: \(-1 \text{ mL} = -1 \times 10^{-6} \text{ m}^3\) (since 1 mL = \(10^{-6}\) m³)

Now substitute these values into the work equation:
\[ W = - (100 \times 10^5) \times (-1 \times 10^{-6}) \]

**Hint:** Ensure you convert all units to SI units before performing calculations.

### Step 4: Perform the Calculation
Now calculate:
\[ W = 100 \times 10^5 \times 10^{-6} = 10 \text{ J} \]

**Hint:** Pay attention to the signs; negative work indicates work done on the system.

### Step 5: Find ΔU
Since we established that \(\Delta U = W\):
\[ \Delta U = 10 \text{ J} \]

**Hint:** The change in internal energy is equal to the work done in this adiabatic process.

### Final Answer
The change in internal energy (ΔU) of the process is:
\[ \Delta U = 10 \text{ J} \]