Name: heat transfer and specific heat
Uploaded: 2025-06-17T07:55:58.000Z
Duration: 2 min 46 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Energy

PS.Chm.7.2

Quantifying Heat

내부 에너지는 열과 일의 상호 변환에 의해 정의됩니다. 하지만 열은 어떻게 측정될까요? 모든 물질은 열 에너지를 갖고 있습니다.

계와 외부의 온도 차이가 존재할 때 열 에너지는 온도가 높은 물질에서 온도가 낮은 물질로 흐릅니다. 이러한 열 에너지 전달을 열 전달이라고도 하며 줄로 측정됩니다. 반면에 온도는 열 에너지의 성질을 설명하며 섭씨 또는 켈빈으로 측정됩니다.

열은 계의 분자의 수와 유형에 영향을 받으나, 온도는 물질에 따른 영향을 받지 않습니다. 열은 열과 계의 온도 변화 사이의 관계를 이용하는 열량계를 이용하여 측정할 수 있습니다. 섭씨 114도의 쇳조각을 상온수에 넣으면 같은 온도가 될 때까지 열이 철에서 물로 흐릅니다.

열의 흐름이 없으면 열 평형 상태가 된 것입니다. 고립계에서 물은 철이 손실하는 만큼의 열을 얻습니다. 하지만 물의 최종 온도는 시작 온도보다 겨우 1도 올랐지만 철은 섭씨 93도 정도 식었습니다.

전달되는 열량은 온도 변화 델타 T에 비례합니다. 비례 상수 C 또는 열 용량"은 계의 온도를 1 켈빈 또는 섭씨 1도 상승시키는 데 필요한 열량입니다. 열 용량은 물질의 종류에 따라 달라집니다.

물처럼 열 용량이 큰 계는 철과 같이 열 용량이 작은 계에 비해 온도를 높이려면 더 많은 열을 흡수해야 합니다. 또한 열 용량은 물질의 질량에 따라 달라집니다. 비열용량 Cs 또는 몰 열용량 Cm은 물질 1 그램, 또는 1몰을 섭씨 1도 올리는 데 필요한 열량을 서술합니다.

따라서 단위는 그램 섭씨 당 줄 또는 몰 섭씨 당 줄로 됩니다. 따라서 계의 비열용량과 온도 변화를 알고 있는 경우 곱셈하여 열 값을 계산할 수 있습니다.

열 정량화

열에너지

현미경으로 보면 열에너지는 원자와 분자의 무작위 운동과 관련된 운동 에너지입니다. 온도는 "뜨거운" 또는 "차가운"을 정량적으로 측정한 것으로, 열에너지의 양에 따라 달라집니다. 물체의 원자와 분자가 빠르게 움직이거나 진동할 때 평균 운동 에너지(KE)(또는 더 높은 열 에너지)가 더 높고 물체가 "뜨거운" 것으로 인식되거나 더 높은 온도에 있는 것으로 설명됩니다. 원자와 분자가 천천히 움직일 때 평균 KE(또는 열에너지)가 낮아지고 물체가 "차가운" 것으로 인식되거나 온도가 더 낮은 것으로 설명됩니다.

화학 반응이나 상 변화(예: 용융 또는 기화)가 발생하지 않는다고 가정할 때, 물질 샘플의 열 에너지 양을 늘리면 온도가 올라가고, 물질 샘플의 열 에너지 양을 줄이면 온도가 증가합니다. 떨어지는 온도.

열

열(q)은 서로 다른 온도에서 두 물체 사이의 열에너지 전달입니다. 열 흐름은 한 몸체의 열 에너지를 증가시키고 다른 몸체의 열 에너지를 감소시킵니다. 열은 자발적으로 뜨거운 곳에서 차가운 곳으로(즉, 한 방향으로만) 흐르며 두 물질이 동일한 온도에 도달할 때까지 계속됩니다. 열의 변화는 온도 변화를 통해 측정됩니다.

열, 일, 에너지의 SI 단위는 줄(J)입니다. 줄(J)은 1뉴턴의 힘으로 물체를 1미터 이동할 때 사용되는 에너지의 양으로 정의됩니다. 영국 물리학자 제임스 프레스콧 줄(James Prescott Joule)의 이름을 따서 명명되었습니다. 1줄은 1kg·m^2/s^2에 해당하며, 1뉴턴미터라고도 합니다. 1킬로줄(kJ)은 1000줄입니다. 정의를 표준화하기 위해 1칼로리는 4.184줄로 설정되었습니다.

열에너지 전달

물질의 열용량(C)은 1°C(또는 이에 상응하는 1켈빈)의 온도 변화(ΔT)를 경험할 때 물질이 흡수하거나 방출하는 열량(q)입니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-01.png" style="height: 40px;" />

열용량은 열을 흡수하거나 방출하는 물질의 유형과 양에 따라 결정됩니다. 따라서 열용량은 광범위한 특성입니다. 그 값은 물질의 양에 비례합니다. 예를 들어, 두 개의 주철 프라이팬의 열용량을 생각해 보세요. 큰 냄비의 열용량은 작은 냄비의 열용량보다 5배 더 큽니다. 왜냐하면 둘 다 같은 재료로 만들어졌지만 큰 냄비의 질량이 작은 냄비의 질량보다 5배 더 크기 때문입니다. 질량이 클수록 더 큰 팬에 더 많은 원자가 존재하므로 모든 원자를 더 빠르게 진동시키려면 더 많은 에너지가 필요합니다. 작은 주철 프라이팬의 열용량은 팬의 온도를 50.0°C(ΔT) 높이는 데 18,140J의 에너지(q)가 필요하다는 것을 관찰하여 구합니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-02.png" style="height: 40px;" />

더 큰 주철 프라이팬은 동일한 물질로 만들어졌지만 온도를 50.0°C(ΔT) 올리려면 90,700J의 에너지(q)가 필요합니다. 더 큰 팬은 더 많은 양의 재료가 동일한 온도 변화를 생성하기 위해 (비례적으로) 더 많은 양의 에너지를 필요로 하기 때문에 (비례적으로) 더 큰 열 용량을 갖습니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-03.png" style="height: 40px;" />

일반적으로 "비열"이라고 불리는 물질의 비열 용량(c)은 물질 1g의 온도를 섭씨 1도(또는 1켈빈) 높이는 데 필요한 열량입니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-04.png" style="height: 40px;" />

비열 용량은 열을 흡수하거나 방출하는 물질의 종류에만 의존합니다. 이는 집중적 특성이므로 물질의 양에 의존하지 않습니다. 예를 들어 작은 주철 프라이팬의 질량은 808g입니다. 따라서 철(팬을 만드는 데 사용되는 재료)의 비열은 다음과 같습니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-05.png" style="height: 40px;" />

대형 프라이팬의 질량은 4040g입니다. 이 팬의 자료를 사용하여 철의 비열을 계산할 수도 있습니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-06.png" style="height: 40px;" />

큰 냄비가 작은 냄비보다 더 무겁지만 둘 다 동일한 재료로 만들어졌기 때문에 둘 다 비열(건축 재료인 철의 경우)에 대한 값은 동일합니다. 비열은 질량당 온도당 에너지 단위로 측정되며 두 가지 광범위한 특성(열과 질량)의 비율에서 파생되는 집중 특성입니다. 집중 특성이기도 한 몰 열용량은 특정 물질의 몰당 열용량이며 단위는 J/mol⋅°C입니다.

물은 상대적으로 높은 비열을 가지고 있습니다(액체의 경우 약 4.2 J/g⋅°C, 고체의 경우 2.09 J/g⋅°C). 대부분의 금속은 비열이 훨씬 낮습니다(보통 1 J/g⋅°C 미만). 물질의 질량(m)과 비열(c)을 알면 열을 얻거나 잃기 전후의 온도 변화(ΔT)를 측정하여 물질에 들어가거나 나가는 열량 q를 결정할 수 있습니다.

<img alt="Eq7" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-07v3.png" style="height: 20px;" />

<img alt="Eq8" src="https://www.jove.com/files/core/CDNSource/lessons/794/794_Equations-08v4.png" style="height: 20px;" />

물질이 열에너지를 얻으면 온도가 상승하고 최종 온도가 초기 온도보다 높으며 T_final − T_initial은 양의 값을 가지며 q 값은 양의 값을 갖습니다. 물질이 열에너지를 잃으면 온도가 감소하여 최종 온도가 초기 온도보다 낮아지고 T_final - T_initial은 음의 값을 가지며 q의 값은 음이 됩니다.

열, 비열, 질량 및 온도 변화 사이의 관계는 다른 세 가지가 알려져 있거나 추론될 수 있는 경우 이러한 양(열뿐만 아니라)을 결정하는 데 사용될 수 있습니다.

이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/5-1-energy-basics">OpenStax Chemistry 2e, Section 5.1: Energy Basics</a> and <a href="https://openstax.org/books/chemistry-2e/pages/5-3-enthalpy">OpenStax Chemistry 2e, Section 5.3: Enthalpy</a>.

열 에너지 

미시적으로 열 에너지는 원자와 분자의 무작위 운동과 관련된 운동 에너지입니다. 온도는 ...

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주요 용어 및 개념

heat transfer and specific heat

Heat transfer and specific heat explain how thermal energy moves and how materials respond to it. Thermal energy is the kinetic energy linked to the random motion of atoms and molecules. Temperature is a measure of how hot or cold a substance is, and it depends on how much thermal energy those particles have.

When atoms and molecules move or vibrate faster, their average kinetic energy is higher. That means the object has more thermal energy and a higher temperature. When they move more slowly, the thermal energy is lower and the temperature drops. If no chemical reaction or phase change, such as melting or vaporizing, occurs, adding thermal energy raises temperature and removing it lowers temperature.

Heat, written as q, is the transfer of thermal energy between two bodies at different temperatures. Heat flow increases the thermal energy of one body and decreases the thermal energy of the other. It moves spontaneously from hot to cold and continues until both substances reach the same temperature. Changes in heat are tracked by changes in temperature.

The SI unit for heat, work, and energy is the joule. One joule is the energy used when a force of 1 newton moves an object 1 meter. It is also equal to 1 kg m^2/s^2, or 1 newton-meter. A kilojoule is 1000 joules, and one calorie is defined as 4.184 joules.

Heat capacity, C, tells how much heat a body absorbs or releases when its temperature changes by 1 degree C, or 1 kelvin. It depends on both the type of substance and the amount present, so it is an extensive property. A large cast iron frying pan has a heat capacity five times greater than a small one because it has five times more mass. More mass means more atoms, so more energy is needed to make all of them vibrate faster.

The small cast iron frying pan in the example takes 18,140 J of energy to rise by 50.0 °C. The larger pan needs 90,700 J to rise by the same amount. Even though both pans are made of the same material, the larger one needs proportionally more energy because it contains more matter.

Specific heat capacity, often called specific heat, is the heat needed to raise 1 gram of a substance by 1 degree Celsius, or 1 kelvin. It depends only on the kind of substance, so it is an intensive property. Using the mass and temperature change of the small pan, the specific heat of iron can be calculated. The large pan gives the same result, even though its mass is greater.

Specific heat is measured in units of energy per temperature per mass. Because it is a ratio of heat and mass, it is intensive even though those two quantities are extensive. The molar heat capacity is another intensive property. It is the heat capacity per mole of a substance and has units of J/mol·°C.

Water has a relatively high specific heat, about 4.2 J/g·°C for liquid water and 2.09 J/g·°C for solid water. Most metals have much lower specific heats, usually less than 1 J/g·°C. If the mass of a substance, its specific heat, and its temperature change are known, the amount of heat entering or leaving it can be found. A positive q means thermal energy is gained and temperature rises. A negative q means thermal energy is lost and temperature falls.

Heat Transfer and Specific Heat

energy basics

How Energy Changes in Chemical Reactions

Chemical reactions change matter and energy at the same time. A match lighting is a simple example. These energy changes are part of everyday life and appear in food, fuels, and industry. Food provides energy through metabolic reactions. The macronutrients in food break down and help keep the body functioning. Fuels such as gasoline, natural gas, and coal are burned to produce energy for transportation, heating, and electricity generation. Industrial chemical reactions also use large amounts...

first law of thermodynamics

Energy Conservation and Internal Energy

Energy conservation describes how energy changes form during chemical and physical changes. Energy can be converted from one form into another, but the energy present before a change still exists in some form after the change is complete. This is the law of conservation of energy. It says energy can neither be created nor destroyed. The law of conservation of matter also applies during chemical change. In most chemical reactions, the total amount of matter does not show a detectable change.

internal energy

Internal Energy, Heat, and Work

Internal energy is the total of all possible kinds of energy in a substance. It is often written as U, and sometimes as E. For a system that changes energy, the important value is the change in internal energy, or ΔU. ΔU is the difference between the final internal energy and the initial internal energy. The exact values of U final and U initial are usually not known, but the first law of thermodynamics only requires ΔU. A positive ΔU means the system gained energy from the surroundings. A...

quantifying heat

Heat transfer and specific heat explain how thermal energy moves and how materials respond to it. Thermal energy is the kinetic energy linked to the random motion of atoms and molecules. Temperature is a measure of how hot or cold a substance is, and it depends on how much thermal energy those particles have. When atoms and molecules move or vibrate faster, their average kinetic energy is higher. That means the object has more thermal energy and a higher temperature. When they move more...

quantifying work

Pressure-Volume Work in Chemistry

Pressure-volume work shows how gas volume changes can transfer energy in chemistry. As a system changes, its internal energy may change too. Energy can move between the system and the surroundings through heat and work. Internal energy, heat, and work are related by an energy equation. Heat depends on a measured temperature change. Work depends on a measured change in volume called pressure-volume work. Work can be defined as a force acting through a distance. Pressure-volume work, also...

enthalpy

Enthalpy and Heat at Constant Pressure

Enthalpy describes heat changes in chemical and physical processes. Chemists use the symbol H for enthalpy. It is defined as a system’s internal energy, E, plus the product of pressure, P, and volume, V. Enthalpy is a state function, so only changes in enthalpy can be measured, not the enthalpy of a substance by itself. For many reactions, the pressure stays constant. Under those conditions, the enthalpy change, ΔH, can be written in a way that includes pressure-volume work. The term PΔV...

thermochemical equations

Heat Changes in Chemical Equations

Heat changes in chemical equations show how much energy a reaction releases or absorbs. At constant pressure, the enthalpy of reaction, or ΔHrxn, is equal to the heat exchanged with the surroundings, qp. Because this value depends on how much reactant takes part, it is an extensive property. The size and sign of ΔHrxn also depend on the reaction itself and on the physical states of the substances involved. An exothermic reaction has a negative ΔHrxn value, while an endothermic reaction has a...

constant pressure calorimetry

Coffee Cup Calorimeter Heat Changes

Coffee cup calorimetry measures heat changes in reactions and physical changes using an insulated calorimeter. The calorimeter is calibrated and designed to limit heat exchange with the outside environment. That makes it possible to measure the heat taken in or released by a substance more accurately, including the energy content of foods. In calorimetry, the system is the substance or substances undergoing change. The surroundings are everything else inside the calorimeter, including the...

constant volume calorimetry

Bomb Calorimeter Heat Measurement

Bomb calorimetry measures the heat released by reactions that produce a lot of energy, especially combustion reactions. A coffee cup calorimeter works at constant pressure and is useful for reactions in solution. A bomb calorimeter works at constant volume and is used for reactions that make large amounts of heat and gaseous products. The word "bomb" refers to the strong, explosive force some reactions can have. In a bomb calorimeter, the volume does not change, so 94V = 0. That means the...

hess's law

Calculating Reaction Heat with Hess's Law

Calculating reaction heat with Hess's law lets chemists find enthalpy changes without measuring every reaction directly. Some reactions are hard or impossible to test in the lab. Even when a reaction can be measured, it is often easier to calculate the heat change from other known enthalpy values. Hess's law says that if a process can be written as the sum of several stepwise processes, the enthalpy change for the total process equals the sum of the enthalpy changes for the steps. This works...

standard enthalpy of formation

Using Standard Enthalpy Values in Chemistry

Enthalpy changes are often listed for reactions that start and end under the same conditions. Chemists use a standard state as a reference set of conditions for comparing properties. In IUPAC terms, the standard state means 1 bar of pressure and 1 M solutions, but it does not set a temperature. Many thermochemical tables still use 1 atm as the reference pressure. Because the difference between 1 bar and 1 atm is very small, enthalpy change usually stays almost the same. A superscripted o in...

enthalpies of reaction

Calculating reaction heat with Hess's law uses standard enthalpies of formation to find the enthalpy change of a reaction. When the formation values for the reactants and products are known, the overall reaction can be broken into simpler stepwise reactions. This approach helps show how the heat change for the full reaction is built from smaller parts. First, the reactants are thought of as being decomposed into their component elements. The enthalpy change for this step is proportional to the...

key terms and concepts

Learn how heat moves between objects, why temperature changes, and how heat capacity and specific heat help measure thermal energy in materials.

Heat Transfer and Specific Heat | JoVE K12

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molecular-comparison-of-gases-liquids-and-solids

Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

surface-tension-capillary-action-and-viscosity

Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded ...

States of Matter and Phase Changes

The internal energy of a substance&#8212;the total kinetic energy of all its molecules and the potential energy of their associated forces&#8212;depends ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Vapor Pressure

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally ...

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Heating and Cooling Curves

When a substance&#8212;isolated from its environment&#8212;is subjected to heat changes, corresponding changes in temperature and phase of the substance ...

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. ...

Use models to explain how changes in energy affect the arrangement and movement of the particles in solids, liquids, and gases, as well as the relative strengths of their intermolecular forces.

PS.Chm.7.1

Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

First Law of Thermodynamics

Energy Conservation

Energy can be converted from one form into another, but all of the energy present before a change occurs always exists in some form ...

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with ...

Thermal Energy&#160;

Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a ...

Quantifying Work

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the ...

Enthalpy

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum ...

Thermochemical Equations

For a chemical reaction (the system) carried out at constant pressure &ndash; with the only work done caused by expansion or contraction &ndash; the ...

Constant Pressure Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process or to measure the heat transferred to or from a ...

Constant Volume Calorimetry

Calorimeters are useful to determine the heat released or absorbed by a chemical reaction. Coffee cup calorimeters are designed to operate at constant ...

using-differential-scanning-calorimetry-to-measure-changes-in-enthalpy

Using Differential Scanning Calorimetry to Measure Changes in Enthalpy

Source: Laboratory of Dr. Terry Tritt &#8212; Clemson University
Differential Scanning Calorimetry (DSC) is a method of thermodynamic analysis based on ...

Hess's Law

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally ...

Standard Enthalpy of Formation

Enthalpy changes are typically tabulated for reactions in which both the reactants and products are at the same conditions. A standard state is a commonly ...

Enthalpies of Reaction

Hess&rsquo;s law can be used to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products ...

Use mathematics and computational thinking to execute simple calorimetric calculations based on the Law of Conservation of Energy.

definition-measurement-pressure-atmospheric-pressure-barometer

Definition and Measurement of Pressure: Atmospheric Pressure, Barometer, and Manometer

Gas pressure is caused by force exerted by gas molecules colliding with the surfaces of objects. Although the force of each collision is very small, any ...

gas-laws-boyle-s-gay-lussac-charles-avogadro-s-and-ideal-gas-law

Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law

Through experiments, scientists established the mathematical relationships between pairs of variables, such as pressure and temperature, pressure and ...

applications-of-the-ideal-gas-law-molar-mass-density-and-volume

Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, &nbsp;suggests that the volume of a given quantity of gas ...

mixtures-of-gases-dalton-s-law-of-partial-pressures-and-mole-fractions

Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other&rsquo;s pressure. Each gas ...

chemical-stoichiometry-gases-using-ideal-gas-law-to-determine

Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles

Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions.

In addition to measuring quantities ...

basic-postulates-kinetic-molecular-theory-particle-size-energy

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For ...

kinetic-molecular-theory-gas-laws-explain-properties-gas

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws ...

kinetic-molecular-theory-molecular-velocities-temperature-kinetic

Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a ...

Use mathematics and computational thinking to explain the relationships among pressure, temperature, volume, and quantity of gas, both qualitatively and quantitatively.

PS.Chm.7.3

Understand the relationship among pressure, temperature, volume, and phase.

Heat Transfer and Specific Heat

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