1 mole of an ideal gas is expanded from an initial pressure of 1 bar to final pressure of 0.1 bar at constant temperature of 273 K. Predict which of the following is not true?

Options

A. `Delta`E = 0
B. `Delta`H = 0
C. PV is constant
D. `Delta S larr 0`

Answer

To solve the problem step by step, we will analyze the situation of the ideal gas expansion and apply the relevant thermodynamic principles.

### Step 1: Understand the Given Information
We have:
- 1 mole of an ideal gas
- Initial pressure (P1) = 1 bar
- Final pressure (P2) = 0.1 bar
- Constant temperature (T) = 273 K

### Step 2: Identify the Thermodynamic Process
Since the temperature is constant, this is an isothermal process. For an ideal gas undergoing an isothermal expansion, we can apply the ideal gas law and the first law of thermodynamics.

### Step 3: Apply the First Law of Thermodynamics
The first law of thermodynamics states:
\[ \Delta U = Q - W \]
Where:
- \(\Delta U\) = change in internal energy
- \(Q\) = heat added to the system
- \(W\) = work done by the system

For an ideal gas, the change in internal energy (\(\Delta U\)) is given by:
\[ \Delta U = n C_v \Delta T \]
Since the process is isothermal (\(\Delta T = 0\)), we have:
\[ \Delta U = 0 \]

### Step 4: Determine the Work Done (W)
In an isothermal process for an ideal gas, the work done (W) can be calculated using:
\[ W = nRT \ln\left(\frac{P_1}{P_2}\right) \]
Substituting the values:
- \(n = 1\) mole
- \(R = 0.08314 \, \text{L bar K}^{-1} \text{mol}^{-1}\)
- \(T = 273 \, \text{K}\)
- \(P_1 = 1 \, \text{bar}\)
- \(P_2 = 0.1 \, \text{bar}\)

Calculating the work done:
\[ W = 1 \times 0.08314 \times 273 \times \ln\left(\frac{1}{0.1}\right) \]
\[ W = 0.08314 \times 273 \times \ln(10) \]
\[ W \approx 0.08314 \times 273 \times 2.3026 \approx 62.36 \, \text{L bar} \quad (\text{convert to Joules if needed}) \]

### Step 5: Analyze the Options
Now, we need to determine which statement is not true based on our findings:
1. \(\Delta U = 0\) (True)
2. \(\Delta H = 0\) (True, since \(\Delta H = \Delta U + \Delta (PV)\) and \(\Delta (PV) = 0\) in isothermal conditions)
3. Volume is constant (Not true, as the volume changes during expansion)
4. \(\Delta S = 0\) (Not true, as entropy increases during expansion)

### Conclusion
The statement that is not true is that the volume is constant. Therefore, the correct answer is that the statement regarding constant volume is incorrect.