For the reaction of one mole of zinc dust with one mole of sulphuric acid in a bomb calorimeter `DeltaU`and`w` correspond to

Options

A. `Delta U lt0, w=0`
B. `Delta U lt 0, w lt0`
C. `Delta U gt0, w=0`
D. `Delta U gt0, w gt0`

Explanation

To solve the problem regarding the reaction of one mole of zinc dust with one mole of sulfuric acid in a bomb calorimeter, we need to analyze the thermodynamic parameters involved, specifically the change in internal energy (ΔU) and the work done (w).

### Step-by-Step Solution:

1. **Understanding the Bomb Calorimeter**:
A bomb calorimeter is a device used to measure the heat of combustion of a substance. It is a sealed container that prevents any exchange of matter with the surroundings.

**Hint**: Remember that in a bomb calorimeter, the system is closed, meaning no gas can escape or enter.

2. **Work Done (w)**:
In a bomb calorimeter, since the system is sealed, there is no volume change during the reaction. Therefore, the work done (w) is zero because work is related to volume change (w = -PΔV).

**Hint**: Consider how work is defined in thermodynamics and how it relates to volume changes in a closed system.

3. **First Law of Thermodynamics**:
According to the first law of thermodynamics, the change in internal energy (ΔU) is given by the equation:
\[ ΔU = Q + W \]
Since we established that \( W = 0 \), we can simplify this to:
\[ ΔU = Q \]

**Hint**: Recall that the first law relates internal energy changes to heat and work.

4. **Heat Exchange (Q)**:
In the reaction between zinc and sulfuric acid, heat is released (exothermic reaction). Therefore, \( Q \) is negative, indicating that the system is losing heat.

**Hint**: Identify whether the reaction is exothermic or endothermic to determine the sign of Q.

5. **Conclusion**:
Since \( W = 0 \) and \( Q < 0 \), we conclude:
- \( ΔU < 0 \) (because \( ΔU = Q \))
- \( W = 0 \)

Thus, the final results are:
- \( ΔU < 0 \)
- \( W = 0 \)

### Final Answer:
- \( ΔU \) is less than zero (ΔU < 0)
- \( W = 0 \)