Radius Of Vapour Bubble In Mechanical Equilibrium In Superheated Liquid Calculator

Formula Used:

\[ r = \frac{2 \cdot \sigma \cdot [R] \cdot (T_{Sat})^2}{P_l \cdot L_v \cdot (T_l - T_{Sat})} \]

Surface Tension (σ):

N/m

Saturation Temperature (T_Sat):

Pressure of Superheated Liquid (P_l):

Enthalpy of Vaporization (L_v):

J/mol

Temperature of Superheated Liquid (T_l):

Radius of Vapor Bubble (r):

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1. What is the Radius of Vapor Bubble Formula?

The formula calculates the radius of a vapor bubble in mechanical equilibrium within a superheated liquid. It's derived from thermodynamic principles and accounts for surface tension, temperature differences, and material properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{2 \cdot \sigma \cdot [R] \cdot (T_{Sat})^2}{P_l \cdot L_v \cdot (T_l - T_{Sat})} \]

Where:

\( r \) — Radius of vapor bubble (m)
\( \sigma \) — Surface tension (N/m)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{Sat} \) — Saturation temperature (K)
\( P_l \) — Pressure of superheated liquid (Pa)
\( L_v \) — Enthalpy of vaporization (J/mol)
\( T_l \) — Temperature of superheated liquid (K)

Explanation: The formula balances surface tension forces against pressure and temperature differences to determine the equilibrium bubble size.

3. Importance of Bubble Radius Calculation

Details: Understanding bubble formation and growth is crucial in various industrial processes including boiling heat transfer, cavitation studies, and chemical processing equipment design.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure temperature of superheated liquid is greater than saturation temperature for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is mechanical equilibrium for a vapor bubble?
A: Mechanical equilibrium occurs when the pressure difference across the bubble interface is balanced by surface tension forces.

Q2: Why is the universal gas constant used in this formula?
A: The gas constant appears because the formula is derived from thermodynamic equilibrium conditions involving vapor pressure relationships.

Q3: What factors affect bubble radius most significantly?
A: Surface tension and temperature difference (T_l - T_Sat) have the most significant impact on bubble size.

Q4: When is this formula applicable?
A: This formula applies to spherical vapor bubbles in homogeneous nucleation within superheated liquids at equilibrium conditions.

Q5: What are typical bubble radius values?
A: Bubble radii typically range from micrometers to millimeters, depending on the liquid properties and superheat conditions.