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To solve this problem, we'll follow these steps:

### Given Data:
- Tank dimensions: \(35 \times 15 \times 10\) meters
- Ullage (distance from top of liquid to the top of tank): 5.7 meters
- Temperature after loading: 27°C
- Density of oil: \(0.8150 \, \text{t/m}^3\) at 15°C
- The vessel was listed 2° to port and trimmed 2.5 meters by the stern
- Temperature increase to 36°C during the voyage

### Part (a): Calculating the Weight of Oil in the Tank
1. **Calculate the volume of oil in the tank:**
   The total height of the tank is 10 meters, and the ullage is 5.7 meters, so the height of the oil column is:
   \[
   \text{Height of oil} = 10 - 5.7 = 4.3 \text{meters}
   \]

   The volume of oil in the tank, ignoring trim and list, is:
   \[
   V = \text{Length} \times \text{Breadth} \times \text{Height} = 35 \times 15 \times 4.3 = 2257.5 \text{m}^3
   \]

2. **Account for list and trim corrections:**
   For a small list and trim, these effects are usually minor, so we can approximate by considering the volume calculated above.

3. **Calculate the weight of oil:**
   Using the density at 15°C:
   \[
   \text{Weight} = V \times \text{Density} = 2257.5 \times 0.8150 = 1840.36 \text{tonnes}
   \]

### Part (b): Calculating the Volume of Oil at 36°C
Oil expands with temperature. The expansion can be accounted for using the coefficient of thermal expansion for the oil. Assuming an average expansion coefficient for oil is about \(0.00064 \, \text{per °C}\), we calculate the change in volume:

1. **Temperature change:**
   \[
   \Delta T = 36 - 27 = 9 \text{°C}
   \]

2. **Calculate the increase in volume:**
   \[
   \Delta V = V \times \text{Coefficient of expansion} \times \Delta T = 2257.5 \times 0.00064 \times 9 = 12.97 \text{m}^3
   \]

3. **New volume at 36°C:**
   \[
   V_{\text{new}} = 2257.5 + 12.97 = 2270.47 \text{m}^3
   \]

### Summary:
(a) The weight of the oil is approximately 1840.36 tonnes.

(b) The volume of oil at 36°C is approximately 2270.47 cubic meters.

Do you want more details on this problem or have any questions? Here are five related questions to expand your understanding:

1. How do changes in temperature affect the density of different fluids?
2. What is the effect of trim and list on the volume calculations in tanks?
3. How does thermal expansion affect different materials differently?
4. What other factors could affect the volume of oil during a voyage?
5. How would changes in atmospheric pressure impact the measurements?

**Tip:** Always account for temperature changes when dealing with fluid volume calculations, as thermal expansion can significantly impact the results.

A boxed shaped tank of dimensions 35 x 15 x 10 meters had an ullage of 5.7 meters at 27°C after completion of loading. Location of ullage port is 1 meter above the deck, 2 meters from aft bulkhead. LBP of the vessel is 120 meters. Vessel was listed 2° to port and trimmed 2.5 meters by stern. Density of oil is 0.8150 t/cbm at 15°C. Find: a) Weight of oil in the tank at the time of taking the ullage. b) Volume of oil in the tank if temperature increases to 36°C during the voyage.

Solve for the weight and volume of oil in a tank given a boxed-shaped tank with dimensions 35 x 15 x 10 meters, ullage of 5.7 meters, and oil density of 0.8150 t/cbm. Learn how temperature changes affect the oil volume during a voyage.

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