Problem 8 - Physics

Question

A typical \(12-V\) car battery can deliver about \(7.5 \times 10^{5} \mathrm{C}\) of charge before dying. This is not very much. To get a feel for this, calculate the maximum number of kilograms of water \(\left(100^{\circ} \mathrm{C}\right)\) that could be boiled into steam \(\left(100^{\circ} \mathrm{C}\right)\) using energy from this battery.

Step-by-Step Solution

Answer

The battery can boil approximately 3.982 kg of water into steam.

Step 1: Determine the Energy from the Battery

The energy stored in a battery can be calculated using the formula \(E = VQ\), where \(E\) is the energy in joules, \(V\) is the voltage (12 V for the car battery), and \(Q\) is the charge (\(7.5 \times 10^{5}\) C).Let's calculate the energy:\[E = 12 \times 7.5 \times 10^{5} = 9.0 \times 10^{6} \text{ J}\].

Step 2: Understand the Energy Required to Boil Water

To convert liquid water at 100°C to steam at 100°C, we use the latent heat of vaporization of water, which is approximately 2260 J/g. This means it takes 2260 joules to convert 1 gram of water into steam.

Step 3: Calculate the Mass of Water Boiled

Now that we know the energy available from the battery, we divide that energy by the latent heat of vaporization to find the mass of water that can be turned into steam:\[ \text{Mass} = \frac{E}{L} = \frac{9.0 \times 10^{6}}{2260} \approx 3982 \text{ g} \].Convert grams to kilograms:\[\text{Mass in kg} = 3982 \text{ g} / 1000 = 3.982 \text{ kg}\].

Key Concepts

Energy Conversion

Energy conversion is the process of changing energy from one form into another. In the context of the original exercise, electrical energy from a car battery is converted into thermal energy to heat water. This process is crucial in understanding how different energy forms can be utilized in practical applications.

• An example of energy conversion is when a battery provides electrical energy, which is then transformed into kinetic energy in an electric motor.
• In our exercise, the battery's electrical energy is used to increase the water's internal energy, leading to phase change without a change in temperature.

Energy conversion is present in nearly all technological devices, helping us utilize the energy stored in various forms to perform work or produce heat.

Latent Heat of Vaporization

The latent heat of vaporization is the amount of energy required to convert a given mass of a liquid into vapor without a change in temperature. In the problem provided, we deal with boiling water at its boiling point to become steam. It helps us understand the energy needed for phase changes, which doesn't involve temperature increases but instead involves change of state.

• The latent heat of vaporization for water is approximately 2260 J/g.
• This value indicates that for each gram of water converted to steam, 2260 Joules of energy is required.
• Understanding this concept is essential for calculating how much energy is needed to induce phase changes in substances.

This concept is vital for various applications, including the design of engines, refrigeration systems, and understanding meteorological processes.

Electric Vehicles

Electric vehicles (EVs) are a prime example of energy conversion, where stored electrical energy in batteries is converted into mechanical energy to drive the vehicle. This involves complex systems and components to effectively manage and convert energy.

• EVs utilize high-capacity batteries to store large amounts of charge, allowing them to travel significant distances.
• Energy conversion efficiency is crucial in EVs, as it impacts the vehicle's range and performance.
• The exercise example, while focused on a smaller car battery, highlights basic principles regarding the stored electrical energy potential in batteries.

Electric vehicles represent a significant advancement in energy conversion technology, offering a cleaner alternative to gasoline-powered cars.

Thermodynamics

Thermodynamics is the study of energy, heat, and its transformations. Understanding thermodynamics is essential when analyzing how energy is transferred and converted, especially in systems where heat exchange occurs, such as engines or power plants. The original exercise uses thermodynamics to determine how electrical energy is used to heat water.

• First law of thermodynamics states that energy cannot be created or destroyed, only transformed, this applies when battery energy is converted to heat.
• The exercise applies concepts such as energy conservation to figure out how much water can be boiled using a given energy input.
• Thermodynamics helps explain the efficiency of energy conversion systems, ensuring minimum losses and optimal energy usage.

In various engineering applications, thermodynamics provides the principles that guide the efficient transfer and transformation of energy.