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# Specific heat capacity - A117

Specific heat capacity
Foundational knowledge article
Document Type Article
Document Identifier 117
Themes
Relevant Class

Material

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## Introduction

Heat capacity, $$C$$, is the material property representing a material’s ability to absorb heat from its external surroundings [1]. It is the ratio of the heat that must be added to or withdrawn from a system for a resulting change in the system’s temperature [2]. Specific heat capacity, $$c_p$$, is defined as the quantity of energy required to raise the internal heat of a material one degree, per unit mass of material, without causing a phase change [3].

## Scope

This page defines heat capacity, explains its significance in composites processing, and provides some typical values. Measurement and modelling methods are briefly discussed. Links to ASTM measurement techniques are provided, but are not discussed in great detail on this page as this is covered in CMH-17 [4] and in the provided ASTM links.

## Significance

In composites processing, the material property of specific heat capacity is involved in several thermal behaviour topics. Examples include the thermal mass of an object and the thermal diffusivity of a material.

## Definition

Heat capacity $$C$$ is the material property representing a material’s ability to absorb heat from its external surroundings [1]. It is the ratio of the heat that must be added to or withdrawn from a system for a resulting change in the system’s temperature [2]. Specific heat capacity $$c_p$$ is defined as the quantity of energy required to raise the internal heat of a material one degree, under specified conditions, per unit mass of material, without causing a phase change [3]. $$c_p$$ is defined under constant pressure conditions, while $$c_v$$ is specific heat under constant volume conditions. For solids, $$c_p$$ and $$c_v$$ are nearly identical in value [5].

Specific heat capacity $$c_p$$ is expressed as$c_p=\frac{1}{m}\cdot\frac{dQ}{dT}$

With,

$$dQ=$$ Energy required to produce the temperature change [J]

$$dT=$$ Temperature change [K]

$$m=$$ Mass of material heated [kg]

### Terminology and Symbol Notation

#### Heat capacity vs. molar heat capacity vs. specific heat capacity

In the literature, the terms heat capacity, molar heat capacity, and specific heat capacity are often used interchangeably. Examining the units can distinguish between them, where specific heat capacity is normalized by a mass unit.

Terminology Units Notes:
Heat Capacity J/K - not to be confused with specific heat capacity
Molar Heat Capacity J/mol·K - normalized in moles, can be converted to specific heat capacity by dividing by the substance molar mass
Specific Heat Capacity J/kg·K - Specific Heat Capacity is Heat Capacity normalized by a mass unit

#### Symbol Notation

In most sources, the mass normalized heat capacity (specific heat capacity) is represented with a small $$c$$ as either $$c_p$$ (constant pressure) or $$c_v$$ (constant volume). At times, it may also be represented with a small $$c$$ or large $$C_p$$ (constant pressure) and $$C_v$$ (constant volume). Examination of mass units should be used to verify what form is presented.

Symbol notation for specific heat capacity
Common reported form $$c_p$$, $$c_v$$
Other reported forms $$c$$, $$C_p$$, $$C_v$$

### Units

The general units of specific heat capacity can be represented as$c_p=\frac{Energy\, unit}{Mass\, unit \cdot Temperature\, unit}$

The following are common International System of Units (SI) and US Customary Units found in the literature for specific heat capacity:

SI Units US Customary Units
Base units J/kg·K BTU/lb·°F
Other common forms J/kg·°C

### Usage of Specific Heat Capacity

The specific heat capacity property is involved in several thermal behaviour topics:

#### Thermal mass

The thermal inertia preventing against temperature fluctuations, thermal mass is determined by the mass of material and its specific heat capacity value.

$$thermal\ mass = m\times c_p$$

Where,

$$m=$$ mass [kg]

$$c_p=$$ specific heat capacity [J/kg·K]

#### Thermal diffusivity

For transient heat transport within a material, specific heat capacity is a significant parameter, where thermal diffusivity is defined as$\alpha=\frac{k}{{\rho}c_p}$

Where,

$$\alpha=$$thermal diffusivity [m2/s]

$$\rho=$$density [kg/m3]

$$c_p=$$ specific heat capacity [J/km·K]

### Typical Property Values

#### Example values for specific heat capacity $$c_p$$ for various materials

Material Typical Value

(SI units)

J/kg·K

Typical Value

(US Customary Units)

BTU/lb·°F

[ref.]
Air (20°C) 1006 0.2403 [6]
Air (100°C) 1011 0.2415 [6]
Nitrogen (20°C) 1041 0.2489 [6]
Nitrogen (100°C) 1043 0.2491 [6]
Copper (pure) 385 0.0920 [7]
Corkboard 1900 0.4538 [7]
Polyethylene (high density) 1850 0.4419 [1]

#### Examples of typical specific heat capacity $$c_p$$ values seen in composite material constituents and materials involved in the manufacturing processing (e.g. tooling)

Composite Use Material Typical Value

(SI units)

J/kg·K

Typical Value

(US Customary Units)

BTU/lb·°F

[ref.]
Reinforcement Fibres Carbon (AS4) 904 0.216 [8]
Glass Fibre (S2) 737 0.176 [9]
Matrix Materials Epoxy Resin (3501-6) 1260 0.3009 [8]
Epoxy Resin (8552) 1025 0.2448 [8]
Tooling Materials Aluminum 902 0.215 [7]
Steel 448-477 0.107-0.114 [7]
Invar 515 0.123 [9]

## Measurement

Specific heat capacity can be measured by differential scanning calorimetry methods (DSC). The following measurement standard for thermal conductivity is recommended by the Composites Materials Handbook - 17 (CMH-17) [4].

Specific heat capacity values can also be obtained by various handbooks, however attention to values at specific temperatures should be cautioned [4].

## Material Microstructure Dependence

For most solids, thermal energy accumulation results from increases in the vibrational energy of the atoms, vibrating constantly with small amplitude but at very high frequencies [1]. The motion of atoms is not independent, instead adjacent atoms are coupled together through atomic bonding creating lattice wave motions that propagate through the material. These elastic-like waves are termed phonons – singular wave is a phonon. With the molecular structure of a given material being fixed (atoms, number of atoms per unit of mass), the vibrational thermal energy for a material consists of a series of these elastic waves within an allowed range of distributions and frequencies for that particular material.

## Process and Environment Dependence

### Temperature

For a particular substance, when the range of temperature change is reasonably small, the value of specific heat capacity is considered approximately constant [3]. The largest changes in a substance's heat capacity in relation to temperature occur at low temperatures, particularly towards absolute zero, with dramatic changes disappearing around room temperature for many solid materials [1]. The minor heat capacity change within the reasonably small temperature ranges experienced during composites processing can be considered a linear function of temperature [10]. Example values for the change in specific heat capacity of a CFRP prepreg material (AS4/8552) at various temperatures measured by Johnston [10] is given below.

#### Example values for specific heat capacity CFRP prepreg (AS4/8552) at various temperature ranges, averaged for three specimens. Source: [10]

Temperature Range

(°C)

Specific Heat Capacity

(J/kg·K)

-40 to -20 883
-20 to 20 1399
20 to 60 1498
60 to 100 1431
100 to 125 1471

For further information in accounting for the changes in specific heat capacity of composite materials with temperature effects, please refer to the modelling section.

### Material State

A material experiences dramatic changes in its heat capacity between its different physical state phases due to changes in molecular mobility and degrees of freedom; simply put, there are differences in the heat capacity values between solid, liquid, and gas phases of a substance. During composites processing, the polymer matrix exhibits phase changes when transitioning between liquid and solid states. In thermoplastics, this occurs during melt solidification, and in thermoset polymers, this occurs during the cure process. In epoxies, the specific heat changes as a function of a degree of cure [10] with a step decrease in specific heat capacity observed at vitrification due to a reduction in molecular mobility [11] in the transitioning from rubbery to glassy behaviour.

## Modelling

The specific heat capacity of a composite material is a combination of the heat capacity of both the matrix resin and the reinforcement fibres. Johnston presented the following lumped and non-lumped models [10] for calculating the specific heat capacity of a combined composite material, while also making considerations for the heat capacity changes with temperature and resin degree of cure:

• Lumped model: Composite specific heat capacity treated as one singular material with matrix (resin) and fibre heat capacities lumped together.
• Non-lumped model: Composite specific heat capacity descretized considering both resin and fibre heat capacities separately first.

### Lumped model

$$C_{Pc}=C_{Pc(0)}+a_{CPc}(T-T_0)+b_{CPc}(x-x_0)$$

Where,

$$C_{Pc(0)}=$$ Nominal specific heat capacity of the composite

$$a_{CPc}=$$ Fitting parameter

$$T=$$ Temperature

$$T_0=$$ Initial or reference temperature

$$b_{CPc}=$$ Fitting parameter

$$x=$$ Degree of cure

$$x_0=$$ Initial or reference degree of cure

### Non-lumped model

#### Resin specific heat capacity is given as:

$$C_{Pr}=C_{Pr(0)}+a_{CPr}(T-T_0)+b_{CPr}(x-x_0)$$

Where,

$$C_{Pr(0)}=$$ Nominal specific heat capacity of the resin

$$a_{CPr}=$$ Fitting parameter

$$T=$$ Temperature

$$T_0=$$ Initial or reference temperature

$$b_{CPr}=$$ Fitting parameter

$$x=$$ Degree of cure

$$x_0=$$ Initial or reference degree of cure

#### Fibre specific heat capacity is given as:

$$C_{Pf}=C_{Pf(0)}+a_{CPf}(T-T_0)$$

Where,

$$C_{Pf(0)}=$$ Nominal specific heat capacity of the fibre

$$a_{CPf}=$$ Fitting parameter

$$T=$$ Temperature

$$T_0=$$ Initial or reference temperature

#### Composite specific heat capacity (ply) is given as:

$$C_{PC}=\frac{V_f\rho_fC_{Pf}+(1-V_f)\rho_rC_{Pr}}{V_f\rho_f+(1-V_f)\rho_r}$$

Where,

$$V_f=$$ Volume fraction fibre

$$\rho_f=$$ Fibre density

$$C_{Pf}=$$ Specific heat capacity fibre

$$\rho_r=$$ Resin density

$$C_{Pr}=$$ Specific heat capacity resin

## Related pages

Introduction to Composites Articles
Foundational Knowledge Articles
Foundational Knowledge Method Documents
Foundational Knowledge Worked Examples
Systems Knowledge Articles
Systems Knowledge Method Documents
Systems Knowledge Worked Examples
Systems Catalogue Articles
Systems Catalogue Objects – Material
Systems Catalogue Objects – Shape
Systems Catalogue Objects – Tooling and consumables
Systems Catalogue Objects – Equipment
Practice Documents
Case Studies
Perspectives Articles

## References

1. [Ref] Callister, William D. (2003). Materials Science and Engineering: An Introduction. John Wiley & Sons, Inc. ISBN 0-471-13576-3.CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
2. [Ref] Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials. Taylor & Francis. ISBN 1-56032-432-5.CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
3. [Ref] Fine, L W et al. (2000). Chemistry for Scientists and Engineers. Saunders golden sunburst series. Saunders College Pub. ISBN 9780030312915.CS1 maint: extra punctuation (link) CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
4. [Ref] Composite Materials Handbook 17 - Polymer Matrix Composites; Guidelines for Characterization of Structural Materials. 1. SAE International on behalf of CMH-17, a division of Wichita State University. 2012. ISBN 978-0-7680-7811-4.CS1 maint: date and year (link)
5. [Ref] Ashby, M.F. (2011). Materials Selection in Mechanical Design. Elsevier. doi:10.1016/c2009-0-25539-5. ISBN 9781856176637.CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
6. [Ref] Slesinger, Nathan Avery (2010). Thermal Modeling Validation Techniques for Thermoset Polymer Matrix Composites (Thesis). doi:10.14288/1.0071063.CS1 maint: uses authors parameter (link)
7. [Ref] Gaskell, David R. (1992). An Introduction to Transport Phenomena in Materials Engineering. Macmillan Publishing Company. ISBN 0023407204.CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
8. [Ref] Hubert, Pascal (1996). Aspects of Flow and Compaction of Laminated Composites Shapes During Cure (Thesis). doi:10.14288/1.0078499.CS1 maint: uses authors parameter (link)
9. [Ref] MatWeb LLC. "MatWeb: Online Materials Information Resource". Retrieved 9 September 2020.CS1 maint: uses authors parameter (link)
10. [Ref] Johnston, Andrew (1997). An integrated model of the development of process-induced deformation in autoclave processing of composite structures (Thesis). doi:10.14288/1.0088805.CS1 maint: uses authors parameter (link)
11. [Ref] Van Assche, G et al. (2001). "Frequency dependent heat capacity in the cure of epoxy resins". 377 (1). doi:10.1016/s0040-6031(01)00547-0. ISSN 0040-6031. Cite journal requires |journal= (help)CS1 maint: extra punctuation (link) CS1 maint: uses authors parameter (link)

## Welcome

Welcome to the CKN Knowledge in Practice Centre (KPC). The KPC is a resource for learning and applying scientific knowledge to the practice of composites manufacturing. As you navigate around the KPC, refer back to the information on this right-hand pane as a resource for understanding the intricacies of composites processing and why the KPC is laid out in the way that it is. The following video explains the KPC approach:

## Understanding Composites Processing

The Knowledge in Practice Centre (KPC) is centered around a structured method of thinking about composite material manufacturing. From the top down, the heirarchy consists of:

The way that the material, shape, tooling & consumables and equipment (abbreviated as MSTE) interact with each other during a process step is critical to the outcome of the manufacturing step, and ultimately critical to the quality of the finished part. The interactions between MSTE during a process step can be numerous and complex, but the Knowledge in Practice Centre aims to make you aware of these interactions, understand how one parameter affects another, and understand how to analyze the problem using a systems based approach. Using this approach, the factory can then be developed with a complete understanding and control of all interactions.

## Interrelationship of Function, Shape, Material & Process

Design for manufacturing is critical to ensuring the producibility of a part. Trouble arises when it is considered too late or not at all in the design process. Conversely, process design (controlling the interactions between shape, material, tooling & consumables and equipment to achieve a desired outcome) must always consider the shape and material of the part. Ashby has developed and popularized the approach linking design (function) to the choice of material and shape, which influence the process selected and vice versa, as shown below:

Within the Knowledge in Practice Centre the same methodology is applied but the process is more fully defined by also explicitly calling out the equipment and tooling & consumables. Note that in common usage, a process which consists of many steps can be arbitrarily defined by just one step, e.g. "spray-up". Though convenient, this can be misleading.

## Workflows

The KPC's Practice and Case Study volumes consist of three types of workflows:

• Development - Analyzing the interactions between MSTE in the process steps to make decisions on processing parameters and understanding how the process steps and factory cells fit within the factory.
• Troubleshooting - Guiding you to possible causes of processing issues affecting either cost, rate or quality and directing you to the most appropriate development workflow to improve the process
• Optimization - An expansion on the development workflows where a larger number of options are considered to achieve the best mixture of cost, rate & quality for your application.