In a large building, oil is used in a steam boiler heating system. The combustion of 1.0 lb of oil provides 2.4 x 10⁷ J (3.4, 3.6) a. How many kilograms of oil are needed to heat 150 kg of water from 22 °C to 100 °C?

Verified step by step guidance

1. Calculate the energy required to heat the water using the formula: $q=m\cdot c\cdot \mathrm{\Delta }T$, where $q$ is the heat energy, $m$ is the mass of the water, $c$ is the specific heat capacity of water (4.18 J/g°C), and $\mathrm{\Delta }T$ is the change in temperature.
2. Convert the mass of water from kilograms to grams to match the units of the specific heat capacity. (1 kg = 1000 g)
3. Determine the change in temperature ($\mathrm{\Delta }T$) by subtracting the initial temperature from the final temperature: $\mathrm{\Delta }T=100°C-22°C$.
4. Calculate the total energy required to heat the water using the values obtained in the previous steps.
5. Determine the mass of oil needed by dividing the total energy required by the energy provided by 1.0 lb of oil (2.4 x 10⁷ J), and convert the mass from pounds to kilograms (1 lb = 0.453592 kg).

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating the energy needed to heat water, as it directly relates the mass of water, the temperature change, and the energy required.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this context, the energy produced by burning oil is converted into thermal energy to heat the water. This concept is essential for determining how much oil is needed based on the energy required to heat the water.

Heat Transfer Calculations

Heat transfer calculations involve determining the amount of energy transferred during heating or cooling processes. In this problem, the total energy required to heat the water can be calculated using the formula Q = mcΔT, where Q is the heat energy, m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature. This calculation is fundamental for finding the amount of oil needed.