The constants `a and b` for the pair silver-lead are `2.50 muV^@ C^(-1) and 0.012mu V^@ C^(-2)` respectively. For a silver-lead thermocouple with colder junction at `0^@ C`,

Options

A. there will be no neutral temperature
B. there will be no inversion temperature
C. there will not be any thermo-emf even if the junctions are kept at different temperatures
D. there will be no current in the thermocouple even if the junctions are kept at different temperature.

Answer

To solve the problem regarding the silver-lead thermocouple with the given constants, we will follow these steps:

### Step 1: Understand the Constants
The constants for the silver-lead thermocouple are given as:
- \( a = 2.50 \, \mu V/°C \)
- \( b = 0.012 \, \mu V/°C^2 \)

### Step 2: Determine the Neutral Temperature
The neutral temperature (\( T_n \)) can be calculated using the formula:
\[ T_n = -\frac{a}{b} \]
Substituting the values of \( a \) and \( b \):
\[ T_n = -\frac{2.50 \, \mu V/°C}{0.012 \, \mu V/°C^2} = -208.33 °C \]

### Step 3: Analyze the Result
Since the neutral temperature is negative, it indicates that the hot junction temperature would be less than the cold junction temperature when the colder junction is at \( 0 °C \). This situation is not feasible as it contradicts the basic principle of thermocouples, where the hot junction must be at a higher temperature than the cold junction.

### Step 4: Determine the Inversion Temperature
The inversion temperature (\( \theta_I \)) is given by:
\[ \theta_I = -\frac{2a}{b} \]
Substituting the values:
\[ \theta_I = -\frac{2 \times 2.50 \, \mu V/°C}{0.012 \, \mu V/°C^2} = -416.67 °C \]
Again, this is negative, indicating that there is no inversion temperature in this case.

### Step 5: Evaluate the Options
1. **Option A**: There will be no neutral temperature. (Correct)
2. **Option B**: There will be no inversion temperature. (Correct)
3. **Option C**: There will not be any thermo-emf even if the junctions are kept at different temperatures. (Incorrect)
4. **Option D**: There will be no current in the thermocouple even if the junctions are kept at different temperatures. (Incorrect)

### Conclusion
The correct options are A and B.

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