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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 17, Problem 24b

In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. How much time is required? Assume that all of the heater's power goes into heating the water.

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Identify the known values: the power of the heater (P) is 200 W, the mass of the water (m) is 0.320 kg, and the specific heat capacity of water (c) is approximately 4,186 J/(kg·°C).
Determine the temperature change needed. Assume the initial temperature of the water is room temperature, about 20°C, and the final temperature is 100°C (boiling point). Calculate the temperature change (ΔT) as ΔT = 100°C - 20°C.
Use the formula for heat energy required to change the temperature of a substance: Q = m * c * ΔT, where Q is the heat energy in joules, m is the mass in kilograms, c is the specific heat capacity, and ΔT is the temperature change in degrees Celsius.
Calculate the total energy required (Q) using the values from the previous steps.
Use the relationship between power, energy, and time: P = Q / t, where P is power in watts, Q is energy in joules, and t is time in seconds. Rearrange the formula to solve for time: t = Q / P. Substitute the known values to find the time required.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Power

Power is the rate at which energy is transferred or converted. In this context, the electric immersion heater has a power rating of 200 watts, meaning it transfers 200 joules of energy per second to the water. Understanding power is crucial for calculating the time required to heat the water.
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Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. For water, this value is approximately 4.18 J/g°C. This concept helps determine the total energy needed to raise the temperature of the water to the desired level.
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Energy Transfer

Energy transfer involves the movement of energy from one system to another. In this scenario, the heater transfers energy to the water, increasing its temperature. Calculating the total energy required and the rate of energy transfer allows us to determine the time needed for heating.
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Textbook Question

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