An explosive with a density of 1.2 g/cm³ has a heat of explosion equal to 900 cal/g. If the heat of explosion of ANFO with density of 0.8 g/cm³ is 950 cal/g, the bulk strength of t... An explosive with a density of 1.2 g/cm³ has a heat of explosion equal to 900 cal/g. If the heat of explosion of ANFO with density of 0.8 g/cm³ is 950 cal/g, the bulk strength of the explosive relative to ANFO is _____. (round off up to 2 decimals)
Understand the Problem
The question is asking us to calculate the bulk strength of a specific explosive relative to ANFO, given their densities and heats of explosion. We will use the provided values to find a ratio of strengths based on the heats of explosion.
Answer
The bulk strength of the explosive relative to ANFO is approximately $1.42$.
Answer for screen readers
The bulk strength of the explosive relative to ANFO is approximately 1.42.
Steps to Solve
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Identify the given values
We have the following data for both explosives:
- Explosive density: ( \rho_{1} = 1.2 , \text{g/cm}^3 )
- Explosive heat of explosion: ( H_{1} = 900 , \text{cal/g} )
- ANFO density: ( \rho_{2} = 0.8 , \text{g/cm}^3 )
- ANFO heat of explosion: ( H_{2} = 950 , \text{cal/g} )
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Calculate the bulk strength of the explosive
The bulk strength ratio relative to ANFO can be calculated using the formula:
[ \text{Relative Strength} = \left( \frac{H_{1} \cdot \rho_{1}}{H_{2} \cdot \rho_{2}} \right) ] -
Insert the values into the formula
Substituting the given values:
[ \text{Relative Strength} = \left( \frac{900 , \text{cal/g} \cdot 1.2 , \text{g/cm}^3}{950 , \text{cal/g} \cdot 0.8 , \text{g/cm}^3} \right) ] -
Perform the calculation
First, calculate the numerator:
[ 900 \times 1.2 = 1080 , \text{cal/cm}^3 ]
Next, calculate the denominator:
[ 950 \times 0.8 = 760 , \text{cal/cm}^3 ]
Now, calculate the relative strength:
[ \text{Relative Strength} = \frac{1080}{760} \approx 1.4211 ] -
Round off the result
Rounding the result to two decimal places gives:
[ \text{Relative Strength} \approx 1.42 ]
The bulk strength of the explosive relative to ANFO is approximately 1.42.
More Information
This ratio helps compare the effectiveness of the explosive relative to ANFO in terms of energy release per volume. A higher value indicates greater strength.
Tips
- Confusing the densities and heats of explosion during calculation.
- Forgetting to convert units properly or neglecting the density's effect on volume.
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