When 1.0 g of gasoline burns, it releases 11 kcal. The density of gasoline is 0.74 g/mL. (3.4, 3.6) b. If a television requires 150 kJ/h to run, how many hours can the television run on the energy provided by 1.0 gal of gasoline?

Verified step by step guidance

1. Convert the volume of gasoline from gallons to milliliters using the conversion factor: 1 gallon = 3785.41 mL.
2. Calculate the mass of gasoline in grams using the density formula: mass = volume x density.
3. Determine the total energy released by burning the calculated mass of gasoline using the given energy release rate: 11 kcal/g.
4. Convert the total energy from kilocalories to kilojoules using the conversion factor: 1 kcal = 4.184 kJ.
5. Calculate the number of hours the television can run by dividing the total energy in kilojoules by the energy consumption rate of the television: 150 kJ/h.

Key Concepts

Energy Conversion

Energy conversion refers to the process of changing energy from one form to another. In this context, it involves converting the chemical energy stored in gasoline into thermal energy when it burns. Understanding this concept is crucial for calculating how much energy is available from a given mass of gasoline.

Units of Energy

Units of energy are essential for understanding how to measure and compare different forms of energy. In this question, energy is given in kilocalories (kcal) and kilojoules (kJ). Knowing the conversion between these units (1 kcal = 4.184 kJ) is necessary to accurately determine how long the television can run on the energy from gasoline.

Density and Volume Calculations

Density is the mass per unit volume of a substance, which is important for converting between mass and volume. In this case, the density of gasoline (0.74 g/mL) allows us to calculate the total mass of gasoline in 1.0 gallon. This calculation is vital for determining the total energy available from the gasoline to power the television.