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: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 19 - Heat and the First Law of Thermodynamics

Problem 16c

Chapter 19, Problem 16c

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?

Verified step by step guidance

Understand the concept of heat capacity: Heat capacity (C) is the amount of heat (Q) required to raise the temperature of an object by 1 °C. For a substance, it is related to its mass and specific heat capacity (c) by the formula:

C = m c

, where m is the mass of the substance and c is its specific heat capacity.

Identify the given values: The mass of water (m) is 38 kg. The specific heat capacity of water (c) is a known constant, approximately

4.186 \, \(\text{J/g°C}\)

4186 \, \(\text{J/kg°C}\)

in SI units.

Substitute the known values into the formula for heat capacity:

C = m c

. Using the mass of water (38 kg) and the specific heat capacity of water (

4186 \, \(\text{J/kg°C}\)

), the equation becomes:

C = 38 \times 4186

Perform the multiplication to calculate the heat capacity: Multiply the mass of water (38 kg) by its specific heat capacity (

4186 \, \(\text{J/kg°C}\)

). This will give the heat capacity in units of

\(\text{J/°C}\)

Interpret the result: The calculated heat capacity represents the total amount of heat required to raise the temperature of 38 kg of water by 1 °C. Ensure the units are consistent and the result is expressed in

\(\text{J/°C}\)

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Key Concepts

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

Heat Capacity

Heat capacity is a physical property of a substance that quantifies the amount of heat energy required to change its temperature by a certain amount, typically 1 °C. It is an extensive property, meaning it depends on the mass of the substance. The formula Q = C∆T illustrates this relationship, where Q is the heat added, C is the heat capacity, and ∆T is the change in temperature.

Specific Heat Capacity

Specific heat capacity is the heat capacity per unit mass of a material, indicating how much heat is needed to raise the temperature of one kilogram of the substance by one degree Celsius. For water, the specific heat capacity is approximately 4.18 J/g°C, which is relatively high compared to many other substances, making it effective for temperature regulation in various applications.

Mass and Temperature Change

In the context of heat capacity, mass and temperature change are critical factors. The mass of the substance directly influences the total heat capacity, as larger masses require more heat to achieve the same temperature change. The temperature change (∆T) is the difference between the initial and final temperatures, and it directly affects the amount of heat (Q) needed, as described by the equation Q = C∆T.

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Related Practice

Textbook Question

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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Textbook Question

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?

Textbook Question

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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Textbook Question

(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?

Textbook Question

A 0.095-kg aluminum sphere is dropped from the roof of a 55-m-high building. If 65% of the thermal energy produced when it hits the ground is absorbed by the sphere, what is its temperature increase?

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Textbook Question

(II) A cube of ice is taken from the freezer at -8.5°C and placed in an 85-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0°C. The final situation is all water at 17.0°C. What was the mass of the ice cube?

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