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 21

Chapter 19, Problem 21

How much heat is needed to melt 26.50 kg of silver that is initially at 25°C?

Verified step by step guidance

Determine the heat required to raise the temperature of the silver from its initial temperature (25°C) to its melting point. Use the formula:

Q = m c ∆ T

, where

m

is the mass of the silver,

c

is the specific heat capacity of silver, and

∆ T

is the temperature change.

Look up the specific heat capacity of silver (

c

) and its melting point. For silver,

c

is approximately 235 J/(kg·°C), and its melting point is 961°C.

Calculate the temperature change

∆ T

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:

Q = m L

, where

L

is the latent heat of fusion for silver. For silver,

L

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.

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.

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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