Coefficient of Thermal Expansion of Real Gas given Difference between Cp and Cv Calculator

Coefficient of Thermal Expansion Formula:

\[ \alpha = \sqrt{\frac{(\delta C_{pv} \times K_T)}{(v \times T)}} \]

Difference in Heat Capacities (δCpv):

J/kg·K

Isothermal Compressibility (K_T):

m²/N

Specific Volume (v):

m³/kg

Temperature (T):

Coefficient of Thermal Expansion (α):

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1. What is Coefficient of Thermal Expansion?

The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. It quantifies the fractional change in size per degree change in temperature at constant pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \alpha = \sqrt{\frac{(\delta C_{pv} \times K_T)}{(v \times T)}} \]

Where:

\( \alpha \) — Coefficient of thermal expansion (1/K)
\( \delta C_{pv} \) — Difference in heat capacities (J/kg·K)
\( K_T \) — Isothermal compressibility (m²/N)
\( v \) — Specific volume (m³/kg)
\( T \) — Temperature (K)

Explanation: This formula relates the thermal expansion coefficient to fundamental thermodynamic properties of real gases.

3. Importance of Thermal Expansion Calculation

Details: Understanding thermal expansion is crucial for engineering applications, material science, and designing systems that operate under varying temperature conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure all inputs are positive values. The calculator will compute the coefficient of thermal expansion in 1/K.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of thermal expansion coefficient?
A: It indicates how much a material expands or contracts per degree temperature change, which is crucial for designing structures and components.

Q2: How does thermal expansion differ between gases and solids?
A: Gases typically have much higher thermal expansion coefficients than solids due to their greater molecular mobility.

Q3: Why is this formula specific for real gases?
A: The formula accounts for intermolecular forces and finite molecular size, which are neglected in ideal gas assumptions.

Q4: What are typical values for thermal expansion coefficients?
A: For gases, values typically range from 0.003 to 0.004 1/K, while solids have much smaller values.

Q5: How does temperature affect thermal expansion?
A: Thermal expansion coefficients generally increase with temperature, though the relationship can be complex for real gases.