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Ch. 19 - Heat and the First Law of Thermodynamics
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 19 - Heat and the First Law of ThermodynamicsProblema 9
Capitolo 19, Problema 9

What is the specific heat of a metal substance if 165 kJ of heat is needed to raise 4.1 kg of the metal from 18.0°C to 37.2°C?

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1
Identify the formula for specific heat: c = QmΔT, where Q is the heat added, m is the mass of the substance, and ΔT is the change in temperature.
Calculate the temperature change: ΔT = Tfinal - Tinitial. Substitute the given values: ΔT = 37.2 - 18.0 (in °C).
Substitute the given values into the formula: Q = 165,000 J (convert kJ to J), m = 4.1 kg, and the calculated ΔT from the previous step.
Rearrange the formula to solve for c: c = QmΔT. Substitute the values into this equation.
Simplify the expression to find the specific heat c in units of J/(kg·°C).

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Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one kilogram of a substance by one degree Celsius. It is a material property that varies between different substances and is crucial for understanding how much energy is needed to change the temperature of a given mass.
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Specific Heat & Temperature Changes

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this context, it is the heat energy supplied to the metal that causes its temperature to rise, which can be calculated using the specific heat formula.
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Overview of Heat Transfer

Thermal Energy Equation

The thermal energy equation, often expressed as Q = mcΔT, relates the heat added (Q) to the mass (m) of the substance, its specific heat capacity (c), and the change in temperature (ΔT). This equation is fundamental for solving problems involving heat transfer and temperature changes in materials.
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Volume Thermal Expansion
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A 215-g sample of a substance is heated to 330°C and then plunged into a 105-g aluminum calorimeter cup containing 185 g of water and a 17-g glass thermometer at 10.5°C. The final temperature is 35.0°C. What is the specific heat of the substance? (Assume no water boils away.)

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The heat capacity, C, of an object is defined as the amount of heat needed to raise its temperature by 1 °C. Thus, to raise the temperature by ∆T requires heat Q given by Q = C∆T. What is the heat capacity of 38 kg of water?

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An average active person consumes about 2500 Cal a day.

(a) What is this in joules?

(b) What is this in kilowatt-hours?

(c) If your power company charges about per kilowatt-hour, how much would your energy cost per day if you bought it from the power company? Could you feed yourself on this much money per day?

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(a) How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water at sea level initially at 11°C? Assume that the part of the pot which is heated with the water is made of 250 g of aluminum, and that no water boils away.

(b) For how long could this amount of energy run a 60-W lightbulb?

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