In a large building, oil is used in a steam boiler heating system. The combustion of 1.0 lb of oil provides 2.4 × 10⁷ J.
b. How many kilograms of oil are needed to change 150 kg of water to steam at 100 °C?

Verified step by step guidance

1. Determine the amount of energy required to convert 150 kg of water to steam at 100 °C. Use the formula for heat energy: $q=m\times L$_v, where $m$ is the mass of water (150 kg) and $L$_v is the heat of vaporization of water (2.26 × 10⁶ J/kg).
2. Calculate the total energy required by substituting the values into the formula: $q=\; 150\; \times \; 2.26\; \times \; 10⁶$. This will give the energy in joules needed to convert the water to steam.
3. Determine how much energy is provided by 1.0 lb of oil. From the problem, 1.0 lb of oil provides 2.4 × 10⁷ J. Convert this energy to the equivalent in kilograms of oil by using the conversion factor: 1 lb = 0.453592 kg.
4. Calculate the mass of oil required to provide the total energy needed. Use the relationship: $m$_oil = q / E_oil, where $q$ is the total energy required (from step 2) and $E$_oil is the energy provided per kilogram of oil (from step 3).
5. Perform the division to find the mass of oil in kilograms. This will give the amount of oil needed to convert 150 kg of water to steam at 100 °C.

Key Concepts

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a substance from liquid to gas at its boiling point. For water, this value is approximately 2.26 x 10⁶ J/kg. Understanding this concept is crucial for calculating how much energy is needed to convert 150 kg of water to steam.

Energy Conversion

Energy conversion refers to the process of changing energy from one form to another. In this context, the energy produced from burning oil is converted into thermal energy to heat water. Knowing the energy content of the oil (2.4 x 10⁷ J per pound) allows us to determine how much oil is needed to provide the required energy for vaporizing the water.

Mass-Energy Relationship

The mass-energy relationship is a principle that relates mass to energy, often expressed through the equation E=mc². In practical terms, this concept helps in understanding how the mass of oil needed can be calculated based on the energy required to heat and vaporize water. This relationship is essential for converting the energy requirements into a mass of oil needed for the heating process.