After a hot shower and dishwashing, there is "no hot water"...

After a hot shower and dishwashing, there is "no hot water" left in the 50 -gal $(185-\mathrm{L})$ water heater. This suggests that the tank has emptied and refilled with water at roughly $10^{\circ} \mathrm{C}$ ( $a )$ How much energy does it take to reheat the water to $50^{\circ} \mathrm{C} ?(b)$ How long would it take if the heater output is 9500 $\mathrm{W} ?$

Key Concepts

Specific Heat Capacity

This is a material-specific property that indicates how much energy is required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is relatively high, meaning that it takes a lot of energy to heat it up compared to many other substances. Understanding this concept is crucial when calculating the energy required for heating processes.

Thermal Energy Calculation

This involves determining the total energy required to raise the temperature of a given mass of a substance by a specified temperature difference. The calculation generally follows the formula Q = m × c × ?T, where Q is the energy, m is the mass, c is the specific heat capacity, and ?T is the temperature change. This key principle underlies many practical situations involving heat transfer.

Power and Energy Relationship

Power is defined as the rate at which energy is transferred or used, usually measured in watts (W), where 1 watt equals 1 joule per second. Understanding the relationship between power, energy, and time is essential for determining how long a process will take to complete given a specific power output. This relationship is generally expressed as Energy = Power × Time.

Unit Conversion

Working with different measurement systems often requires converting units to ensure consistency in calculations, such as converting gallons to liters or adjusting temperature scales. Mastery of unit conversion is essential in physics and engineering for accurate computation and interpretation of results.

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