Question 62

The Correct Answer is D ### Why Option D (6,144) is Correct The problem asks for the expected volume of the cargo (gasoline) at the discharge port, given an initial loaded volume, a change in temperature, and a volume correction factor (VCF). Liquids expand when heated, so we expect the volume to increase. **1. Calculate the Temperature Change ($\Delta T$):** $$\Delta T = \text{Discharge Temperature} - \text{Loading Temperature}$$ $$\Delta T = 90^\circ \text{F} - 50^\circ \text{F} = 40^\circ \text{F}$$ **2. Calculate the Total Volume Change Percentage (Expansion):** The volume correction factor (VCF) given is $0.0006$ (which represents the change in volume per barrel per degree Fahrenheit). The total fractional change is calculated by multiplying the VCF by the temperature change. $$\text{Total Fractional Change} = \text{VCF} \times \Delta T$$ $$\text{Total Fractional Change} = 0.0006 \times 40 = 0.024$$ *(Note: This means the volume increased by 2.4%.)* **3. Calculate the Expected Unloaded Volume ($\text{V}_{\text{unload}}$):** The new volume is the original volume plus the expansion. $$\text{V}_{\text{unload}} = \text{Loaded Volume} \times (1 + \text{Total Fractional Change})$$ $$\text{V}_{\text{unload}} = 6,000 \text{ barrels} \times (1 + 0.024)$$ $$\text{V}_{\text{unload}} = 6,000 \text{ barrels} \times 1.024$$ $$\text{V}_{\text{unload}} = 6,144 \text{ barrels}$$ Thus, 6,144 barrels would be expected at the discharge port. *** ### Why Other Options Are Incorrect **A) 5,856:** This result would be obtained if the temperature had decreased by $40^\circ \text{F}$ (cooling, resulting in shrinkage), or if the total change calculation was subtracted: $6,000 \times (1 - 0.024) = 5,856$. Since the temperature increased from $50^\circ \text{F}$ to $90^\circ \text{F}$, the volume must increase, not decrease. **B) 5,982:** This result is significantly lower than the expected increase and does not correspond to a logical error in the calculation (it implies a temperature change of only $30^\circ \text{F}$ if using an incorrect negative VCF of $0.0001$). More simply, it is incorrect because it implies shrinkage, which is physically impossible when heating a liquid. **C) 6,018:** This result is obtained if the expansion is significantly underestimated. For instance, calculating the expansion based on only $30^\circ \text{F}$ of temperature change: $6,000 \times 0.0006 \times 30 = 108$ barrels. $6,000 + 108 = 6,108$ (still incorrect). A calculation error resulting in a much smaller expansion would lead to this answer, but it is too low based on the provided data.