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

Giancoli Douglas 5th edition

Ch. 19 - Heat and the First Law of Thermodynamics

Problema 38b

Capitolo 19, Problema 38b

A 1.0-L volume of air initially at 3.5 atm of (gauge)pressure is allowed to expand isothermally until the (gauge) pressure is 1.0 atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating at constant volume. How much work does the 1.0 L of air do in this process?

Guida verificata passo dopo passo

Step 1: Understand the problem and identify the process. The problem involves three thermodynamic processes: (1) isothermal expansion, (2) isobaric compression, and (3) isochoric heating. The goal is to calculate the total work done by the air during these processes.

Step 2: Write the formula for work done during isothermal expansion. For an isothermal process, the work done is given by:

W = n R T ln (\frac{P_{i}}{P_{f}})

, where

n

is the number of moles,

R

is the gas constant,

T

is the temperature, and

P_{i}

and

P_{f}

are the initial and final pressures, respectively. Use the given pressures and assume the temperature remains constant.

Step 3: Calculate the work done during the isobaric compression. For an isobaric process, the work done is given by:

W = P_{f} \cdot (V_{f} - V_{i})

, where

P_{f}

is the constant pressure, and

V_{i}

and

V_{f}

are the initial and final volumes. Use the given data to calculate the change in volume during this step.

Step 4: Note that no work is done during the isochoric heating process. In an isochoric process, the volume remains constant, so the work done is zero:

W = 0

. This simplifies the calculation for this step.

Step 5: Add the work contributions from all three processes. The total work done by the air is the sum of the work done during the isothermal expansion, the isobaric compression, and the isochoric heating. Use the results from Steps 2, 3, and 4 to find the total work done.

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Isothermal Process

An isothermal process occurs when a system undergoes a change at a constant temperature. In the context of gases, this means that the internal energy remains constant, and any heat added to the system is used to do work. For an ideal gas, the work done during an isothermal expansion can be calculated using the formula W = nRT ln(Vf/Vi), where Vf and Vi are the final and initial volumes, respectively.

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Entropy & Ideal Gas Processes

Work Done by a Gas

The work done by a gas during expansion or compression is defined as the product of pressure and the change in volume. For a constant pressure process, the work can be calculated using W = PΔV, where ΔV is the change in volume. In the case of isothermal expansion and compression, the work done can vary significantly depending on the initial and final pressures and volumes.

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Calculating Work Done on Monoatomic Gas

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In thermodynamic processes, this law can be expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. Understanding this principle is crucial for analyzing energy transfers in the described process.

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The First Law of Thermodynamics

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