Name: ideal gas heat capacity differences
Uploaded: 2023-04-30T12:32:12.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

Heat Capacities of an Ideal Gas II

異なる熱力学的プロセスを経ることができる、異なる温度の理想気体で満たされた2つの同一のフラスコを考えてみましょう。
一定体積プロセスで、最初のフラスコのガス温度が2番目のフラスコの温度と等しくなるように上昇するとします。
そうすると、その内部エネルギーは熱変化と同じになり、モル熱容量で表すことができます。
定圧プロセスでは、温度が同じ量だけ上昇すると、何らかの作業が行われるとシステムの内部エネルギーが変化します。
内部エネルギーは状態関数であるため、システムの内部エネルギー変化は両方のプロセスで同じです。
微分形式の理想気体方程式を使用すると、行われた作業を温度変化の観点から記述できます。
両側の共通要因を相殺することにより、両方のプロセスのモル熱容量間の関係が得られます。
ここで、Rは普遍的なガス定数であるため、一定圧力プロセス下での理想ガスのモル熱容量は、一定体積プロセス下でのモル熱容量よりも常に大きくなります。

<ol>
	<li>ヤング、HD、フリードマン、RA(2012)。現代物理学と大学物理学。カリフォルニア州サンフランシスコ:Pearson.637-638。</li>
	<li>OpenStaxです。(2019). 大学物理学 Vol.2.【Web版】。126-127 <a href="https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas"から取得>https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas</a></li>
</ol>

理想気体の熱容量 ii

一定の体積条件で熱力学的プロセスを受ける系の場合、吸収された熱は系の内部エネルギーを増加させるためだけに使用され、いかなる仕事にも使用されません。 一定の圧力条件下で熱力学的プロセスが行われる系の場合、吸収される熱量は内部エネルギー (温度の関数として) を増加させるためだけでなく、何らかの仕事を行うためにも使用されます。 モル熱容量は、1 モルの気体の温度を 1 単位上昇させるのに必要な熱量です。 吸収された熱の一部は仕事をするために使用されるため、温度を 1 単位上昇させるには定圧下の系にさらに熱を加える必要があります。定圧プロセスのモル熱容量は常に一定体積のモル熱容量よりも大きくなります。 したがって、熱力学の第一法則に基づいた導出から、次の関係が得られます。

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

したがって、2 つのモル熱容量の差は定数であり、普遍気体定数 R に等しくなります。 理想気体定数またはモル気体定数とも呼ばれます。 その値は約 8.314 で、モル比熱容量 J/mol⋅K と同じ SI 単位で表されます。 たとえば、He の場合、Cp と CV の測定値は 20.78 J/mol· ;K および 12.47 J/mol·K それぞれ。 それらの違いは次のとおりです。 8.31 J/mol·K は R. に近い値です。

理想気体の熱容量 II

一定体積条件で熱力学的プロセスを経るシステムの場合、吸収された熱はシステムの内部を増加させるためだけに使用されます...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

The First Law of Thermodynamics

熱力学第一法則

KEY TERMS AND CONCEPTS

主要用語と概念

ideal gas heat capacity differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case.

At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at constant pressure than at constant volume.

From the first law of thermodynamics, the two molar heat capacities are related by a simple equation. The difference between the constant-pressure heat capacity, Cp, and the constant-volume heat capacity, Cv, is a constant. That constant is the universal gas constant, R, also called the ideal gas constant or molar gas constant.

The value of R is about 8.314 and it uses the same SI unit as molar specific heat capacity, J/mol·K. A helium example shows this relationship clearly. For He, Cp is 20.78 J/mol·K and Cv is 12.47 J/mol·K. Their difference is 8.31 J/mol·K, which is close to R.

Ideal Gas Heat Capacity Differences

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heat capacities of an ideal gas ii

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Ideal Gas Heat Capacity Differences | JoVE K12

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Ideal Gas Heat Capacity Differences

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