Review problem. A certain storm cloud has a potential of 1.00 ×10^8 V relative to a tree. If, du

step 1 Here we have the energy transferred is given by half Q delta V equals half times total charge tr

Review problem. A certain storm cloud has a potential of...

Review problem. A certain storm cloud has a potential of $1.00 \times 10^{8} \mathrm{V}$ relative to a tree. If, during a lightning storm, $50.0 \mathrm{C}$ of charge is transferred through this potential difference and $1.00 \%$ of the energy is absorbed by the tree, how much sap in the tree can be boiled away? Model the sap as water initially at $30.0^{\circ} \mathrm{C}$. Water has a specific heat of $4186 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C},$ a boiling point of $100^{\circ} \mathrm{C},$ and a latent heat of vaporization of $2.26 \times 10^{6} \mathrm{J} / \mathrm{kg}$.

Key Concepts

Latent Heat of Vaporization

Latent heat of vaporization is the energy required to convert a substance from its liquid phase to its vapor phase without a temperature change. This concept is particularly relevant once the substance reaches its boiling point, as any additional energy provided is used to overcome intermolecular forces rather than increase temperature. It is crucial in estimating the amount of material that can undergo phase change when a given amount of energy is absorbed.

Specific Heat Capacity

Specific heat capacity is a property of a substance that indicates how much energy is needed to raise the temperature of a unit mass by one degree Celsius. It provides a measure of a substance’s ability to store thermal energy. In contexts where heat is absorbed or released, specific heat is used to calculate temperature changes before any phase change occurs.

Energy Transfer Efficiency

Energy transfer efficiency refers to the fraction of the total energy that is actually available for a specific process after accounting for losses. In many real-world scenarios, only a small percentage of the initial energy is usefully transferred, while the rest is lost to the surroundings. This concept is important when determining the net energy absorbed by an object, as seen when converting electrical energy into thermal energy in the tree.

Electrical Potential Energy

This concept involves the energy stored by virtue of an electric field acting on a charge. When a charge moves through a potential difference, it gains or loses energy equal to the product of the charge and the potential difference (E = Q × V). This energy conversion is fundamental in understanding how electrical energy can be transformed into other forms, such as thermal energy in this problem.

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