Question 57

The Correct Answer is A ### 1. Explanation for why Option A (327,533) is correct The problem requires calculating the expected unloaded volume in gallons by correcting the loaded volume (8,000 barrels) for the change in temperature (cooling). Since the liquid cooled down from $97^\circ F$ to $55^\circ F$, the volume contracted. **Step 1: Determine the Temperature Difference ($\Delta T$)** The loaded temperature is $97^\circ F$ (36°C) and the discharge temperature is $55^\circ F$. $$\Delta T = T_{load} - T_{unload}$$ $$\Delta T = 97^\circ F - 55^\circ F = 42^\circ F$$ **Step 2: Calculate the Volume Correction Factor (VCF)** The VCF is calculated using the given coefficient of thermal expansion ($\alpha = 0.0006$). Since the cargo cooled down, the correction factor must be less than 1. $$VCF = 1 - (\alpha \times \Delta T)$$ $$VCF = 1 - (0.0006 \times 42)$$ $$VCF = 1 - 0.0252$$ $$VCF = 0.9748$$ *(Note: The API gravity of 54° is typically used to find a standardized VCF from ASTM tables, but since a specific VCF factor (0.0006) is provided in the problem, we use that simplified calculation.)* **Step 3: Calculate the Unloaded Volume in Barrels** $$V_{unload, bbl} = V_{load} \times VCF$$ $$V_{unload, bbl} = 8,000 \text{ bbl} \times 0.9748$$ $$V_{unload, bbl} = 7,798.4 \text{ barrels}$$ **Step 4: Convert Barrels to Gallons** (Standard conversion: 1 barrel = 42 U.S. gallons) $$V_{unload, gal} = 7,798.4 \text{ bbl} \times 42 \text{ gal/bbl}$$ $$V_{unload, gal} = 327,532.8 \text{ gallons}$$ Rounding to the nearest whole number gives **327,533**. --- ### 2. Explanation for why the other options are incorrect **B) 344,484** This option results from incorrectly applying the volume correction factor by *adding* the expansion amount instead of subtracting it (treating the cooling as a warming/expansion event). Error calculation: $V_{load} \times (1 + 0.0252) = 8,000 \times 1.0252 = 8,201.6$ barrels. $8,201.6 \text{ bbl} \times 42 \text{ gal/bbl} = 344,467.2$ gallons. This closely matches 344,484. **C) 428,890** This volume is approximately 31% higher than the correct answer. The initial loaded volume is 336,000 gallons ($8,000 \times 42$). This option represents a major calculation error, likely involving a significant error in the volume conversion factor or an incorrect starting volume base. **D) 451,110** This option is significantly higher than the initial loaded volume of 336,000 gallons. It represents an error that is too large to be explained by a simple misuse of the VCF or $\Delta T$. This could result from confusing mass/weight calculations with volume, or using an entirely incorrect volume conversion standard.