Textbook Question
An iron boiler of mass 180 kg contains 710 kg of water at 18°C. A heater supplies energy at the rate of 58,000 kJ/h. How long does it take for the water to all have changed to steam?
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Ch. 19 - Heat and the First Law of Thermodynamics
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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Table of contents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
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Giancoli Douglas 5th editionCh. 19 - Heat and the First Law of ThermodynamicsProblem 21
Giancoli Douglas 5th editionCh. 19 - Heat and the First Law of ThermodynamicsProblem 21Chapter 19, Problem 21
How much heat is needed to melt 26.50 kg of silver that is initially at 25°C?
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Determine the heat required to raise the temperature of the silver from its initial temperature (25°C) to its melting point. Use the formula: , where is the mass of the silver, is the specific heat capacity of silver, and is the temperature change.
Look up the specific heat capacity of silver () and its melting point. For silver, is approximately 235 J/(kg·°C), and its melting point is 961°C.
Calculate the temperature change by subtracting the initial temperature (25°C) from the melting point (961°C). Substitute the values into the formula to find the heat required to raise the temperature.
Determine the heat required to melt the silver once it reaches its melting point. Use the formula: , where is the latent heat of fusion for silver. For silver, is approximately 88,000 J/kg.
Add the heat required to raise the temperature to the melting point and the heat required to melt the silver. This total is the amount of heat needed to melt 26.50 kg of silver starting at 25°C.
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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 of thermal energy moving from one object or substance to another due to a temperature difference. In the context of melting silver, heat is absorbed by the silver to overcome the forces holding its solid structure together, transitioning it into a liquid state. This process is governed by the principles of thermodynamics.
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Latent Heat of Fusion
Latent heat of fusion is the amount of heat required to change a substance from solid to liquid at its melting point without changing its temperature. For silver, this value is essential to calculate the total heat needed to melt the given mass. It reflects the energy needed to break the bonds between silver atoms in the solid state.
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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. In this scenario, it is important to first raise the temperature of silver from its initial temperature (25°C) to its melting point (961.8°C) before melting it. This concept helps in calculating the total heat required for the entire process.
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Related Practice
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?
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Textbook Question
High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from your body if you melt 1.0 kg of -15°C snow using a stove and drink the resulting 1.0 kg of water at 2°C, which your body has to warm to 37°C.
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Textbook Question
What mass of steam at 100°C must be added to 1.00 kg of ice at 0°C to yield liquid water at 30°C?
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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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