91Ó°ÊÓ

Heat transfer is the process by which thermal energy moves from one place to another. Specifically, it is the movement of heat from a hotter object to a cooler one until thermal equilibrium is reached. In the context of our exercise, the hot water heater transfers heat to the water to raise its temperature. There are several methods of heat transfer:

• Conduction: Heat moves through a material or between materials that are in direct contact.
• Convection: Heat causes fluid (such as water or air) to move, carrying the heat with it.
• Radiation: Heat is transferred through electromagnetic waves without needing a medium.

Understanding the mode of heat transfer is crucial as it helps determine the efficiency and effectiveness of heating processes. Water heaters typically convert electrical or gas energy into thermal energy, which is then transferred to the water primarily through convection.

Specific heat capacity is a crucial concept in understanding how substances absorb heat. It is defined as the amount of heat needed to change the temperature of one unit mass of a substance by one degree. For water, the specific heat capacity is relatively high, which means it requires more energy to change its temperature compared to many other substances.

• In metric units, the specific heat capacity for water is approximately 4.186 kJ/(kg°C).
• In Imperial units, it is about 1 Btu/(lb°F).

This means that for the water heater in the exercise, a significant amount of energy is required to raise the temperature of the water by a certain number of degrees. Calculations involving specific heat capacity help determine how much heat energy (Q) is needed based on the mass (m) of the water and the temperature change ( \( \Delta T \) ).

Energy conversion is one of the cornerstones of thermodynamics, particularly relevant in appliances like water heaters. In this context, energy conversion refers to transforming electrical or other forms of energy into thermal energy. Water heaters typically operate on electrical power or gas and transform these energy sources into the heat needed to increase the temperature of the water.

The power of the water heater (P) is pivotal in determining how quickly the heat energy is supplied. For instance, in the exercise:

• The nonmetric version of the heater has a power of 2.0 × 10 \( ^5 \) Btu/h.
• The metric system uses a power rating of 59 kW.

Once the energy (Q) required to heat the water is known, the time (t) taken to supply this energy can be determined using the formula \( t \)\( = \)\( \frac{Q}{P} \), illustrating the direct relationship between energy conversion rate and the heating time.

Water heating calculations involve determining the time required to elevate water temperature using a given heater. The first step is identifying the temperature change ( \( \Delta T. \) ) needed. In our exercise:

• Nonmetric: From 70°F to 100°F, giving a \( \Delta T = 30^ \circ F \).
• Metric: From 21°C to 38°C, so \( \Delta T = 17^ \circ C \).

Next, convert the volume of water to mass (gallons to pounds or liters to kilograms). Following this, use the specific heat capacity to compute the heat energy (Q) needed with \\( Q = mc \Delta T \).With the calculated heat energy and the rated power of the heater, time (t) is determined by using \\( t = \frac{Q}{P} \). Finally, convert the time into workable units (hours to minutes, seconds to minutes) for practical understanding, as shown in the step-by-step solutions of the exercise.