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 19.31

Chapter 19, Problem 19.31

(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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Calculate the heat lost by the water and the calorimeter. Use the formula \(Q = mc\Delta T\), where \(m\) is the mass, \(c\) is the specific heat capacity (for water, \(c = 4.18 \, \text{J/g}^{\circ}\text{C}\) and for aluminum, \(c = 0.900 \, \text{J/g}^{\circ}\text{C}\)), and \(\Delta T\) is the change in temperature.

Calculate the heat gained by the ice to raise its temperature from -8.5°C to 0°C using the same heat formula. For ice, use the specific heat capacity \(c = 2.09 \, \text{J/g}^{\circ}\text{C}\).

Calculate the heat required to melt the ice at 0°C. Use the formula \(Q = mL\), where \(m\) is the mass of the ice and \(L\) is the latent heat of fusion for ice (\(L = 334 \, \text{J/g}\)).

Set up the equation where the total heat lost by the water and the calorimeter equals the total heat gained by the ice. This includes the heat to raise the temperature of the ice to 0°C and the heat to melt the ice.

Solve the equation for the mass of the ice, \(m_{\text{ice}}\). This will give you the mass of the ice cube initially placed in the calorimeter.

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Key Concepts

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

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object to another due to a temperature difference. In this scenario, heat flows from the warmer water and aluminum calorimeter to the colder ice cube, causing the ice to melt and the water to cool down until thermal equilibrium is reached.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. Each material has a unique specific heat capacity, which influences how much energy is absorbed or released during temperature changes. In this problem, the specific heat capacities of water and aluminum are crucial for calculating the heat exchanges.

Phase Change

Phase change refers to the transition of a substance from one state of matter to another, such as from solid to liquid. During the melting of ice, energy is absorbed without a change in temperature until the ice completely transitions to water. This latent heat of fusion must be accounted for when determining the mass of the ice cube in the calorimetry problem.

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Textbook Question

(II) A 0.40-kg iron horseshoe just forged and very hot (Fig. 19–31), is dropped into 1.35 L of water in a 0.30-kg iron pot initially at 20.0°C. If the final equilibrium temperature is 25.0°C, estimate the initial temperature of the hot horseshoe..

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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

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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Textbook Question

If 3.40 x 10⁵ J of energy is supplied to a container of liquid oxygen at -183° C , how much oxygen can evaporate?

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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