The key difference between isothermal and adiabatic elasticity is that isothermal elasticity occurs when the temperature is kept constant, whereas adiabatic elasticity occurs when no net heat exchange occurs between the system and its surrounding.
Isothermal elasticity is the type of elasticity that occurs when the gas is compressed in a way that the temperature is kept constant under isothermal conditions compared to the corresponding volume elasticity. Adiabatic elasticity is the type of elasticity that occurs when the gas is compressed in a way that no heat is allowed to enter or leave the system under adiabatic conditions compared to the corresponding elasticity.
CONTENTS
1. Overview and Key Difference
2. What is Isothermal Elasticity
3. What is Adiabatic Elasticity
4. Isothermal vs Adiabatic Elasticity in Tabular Form
5. Summary – Isothermal vs Adiabatic Elasticity
What is Isothermal Elasticity?
Isothermal elasticity is the type of elasticity that occurs when the gas is compressed in a way that the temperature is kept constant under isothermal conditions compared to the corresponding volume elasticity. This is denoted by KT.
When considering a perfect gas at a constant temperature,
pV = constant
where p is pressure and V is the volume.
By differentiating the above statement,
P + V.dp/dV = 0
P = – dp/(dV/V) = measure of volume elasticity.
Therefore, under isothermal conditions,
KT = p
What is Adiabatic Elasticity?
Adiabatic elasticity is the type of elasticity that occurs when the gas is compressed in such a way that no heat is allowed to enter or leave the system under adiabatic conditions compared to the corresponding elasticity. This term is denoted by Kϕ.
When considering a perfect gas under adiabatic elasticity,
pVγ = constant
by differentiating the above expression we get,
p. γVγ-1 + Vγ(dp/dV/V) = 0
γp = -dp/(dV/V) = measures the volume elasticity.
Therefore,
Kϕ = γp
What is the Difference Between Isothermal and Adiabatic Elasticity?
Isothermal elasticity is the type of elasticity that occurs when the gas is compressed in such a way that the temperature is kept constant under isothermal conditions compared to the corresponding volume elasticity. Meanwhile, adiabatic elasticity is the type of elasticity that occurs when the gas is compressed in such a way that no heat is allowed to enter or leave the system under adiabatic conditions compared to the corresponding elasticity. So, the key difference between isothermal and adiabatic elasticity is that isothermal elasticity occurs when the temperature is kept constant, whereas adiabatic elasticity occurs when there is no net heat exchange between the system and its surrounding.
The below infographic presents the differences between isothermal and adiabatic elasticity in tabular form for side by side comparison.
Summary – Isothermal vs Adiabatic Elasticity
Isothermal and adiabatic elasticities are important terms in physical chemistry. Isothermal elasticity is the type of elasticity that occurs when the gas is compressed in such a way that the temperature is kept constant under isothermal conditions compared to the corresponding volume elasticity. On the other hand, adiabatic elasticity is the type of elasticity that occurs when the gas is compressed in such a way that no heat is allowed to enter or leave the system under adiabatic conditions compared to the corresponding elasticity. Thus, the key difference between isothermal and adiabatic elasticity is that isothermal elasticity occurs when the temperature is kept constant, whereas adiabatic elasticity occurs when there is no net heat exchange between the system and its surrounding.
Reference:
1. “What Do You Mean by Adiabatic and Isothermal Elasticities What Is the Ratio of Adiabatc to Isothermal Elasticity and Why k80f6ctt -Physics.” TopperLearning.
2. Workum, K Van, et al. “Isothermal Stress and Elasticity Tensors for Ions and Point Dipoles Using Ewald Summations.” NIST, 17 Feb. 2017.
3. “What Is an Adiabatic Process? What Is an Adiabatic System?.” Quora.
Image Courtesy:
1. “Thermodynamic system01b” By Adwaele at English Wikipedia (CC BY-SA 3.0) via Commons Wikimedia
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