A gas with initial state variables p1, V1, and T1 expands isothermally until V2 = 2V1. What are T1?

Ch 18: A Macroscopic Description of Matter

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 18: A Macroscopic Description of Matter

문제 28a

18장, 문제 28a

A gas with initial state variables p₁, V₁, and T₁ expands isothermally until V₂= 2V₁. What are T₁?

검증된 단계별 안내

Step 1: Recognize that the process is isothermal, meaning the temperature remains constant throughout the expansion. Therefore, T₁ = T₂.

Step 2: Recall the ideal gas law, which is expressed as

PV = nRT

, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Step 3: Since the temperature is constant (T₁ = T₂), the product of pressure and volume remains constant during the expansion. This is expressed as

p₁V₁ = p₂V₂

Step 4: Substitute the given relationship for the final volume,

V₂ = 2V₁

, into the equation

p₁V₁ = p₂V₂

to find the relationship between p₁ and p₂.

Step 5: Conclude that since the temperature remains constant, T₂ = T₁. No further calculation is needed for T₂.

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주요 개념

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Isothermal Process

An isothermal process is a thermodynamic process in which the temperature of the system remains constant. For an ideal gas, this means that any heat added to the system is used to do work, rather than increasing the internal energy. In this scenario, since the gas expands isothermally, the temperature T₂ will equal the initial temperature T₁.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law helps in understanding how changes in volume and temperature affect the state of the gas during the isothermal expansion.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This relationship implies that if the volume of a gas increases, its temperature must also increase, provided the pressure does not change. In the context of the isothermal expansion, while the volume doubles, the temperature remains constant, reinforcing the concept that T₂ = T₁.