Change In Internal Energy Of Lumped Body Calculator

Formula Used:

\[ \Delta U = \rho \cdot c \cdot V_T \cdot (T_o - t_f) \cdot (1 - \exp(-Bi \cdot Fo)) \]

Density (ρ):

kg/m³

Specific Heat (c):

J/kg·K

Total Volume (V_T):

m³

Initial Temperature (T_o):

Fluid Temperature (t_f):

Biot Number (Bi):

Fourier Number (Fo):

Change in Internal Energy (ΔU):

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1. What is Change in Internal Energy of Lumped Body?

The change in internal energy of a lumped body represents the energy variation within a thermodynamic system. It quantifies the energy required to create or prepare the system in any given internal state, considering heat transfer processes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Delta U = \rho \cdot c \cdot V_T \cdot (T_o - t_f) \cdot (1 - \exp(-Bi \cdot Fo)) \]

Where:

\( \Delta U \) — Change in internal energy (J)
\( \rho \) — Density of the material (kg/m³)
\( c \) — Specific heat capacity (J/kg·K)
\( V_T \) — Total volume of the body (m³)
\( T_o \) — Initial temperature (K)
\( t_f \) — Fluid temperature (K)
\( Bi \) — Biot number (dimensionless)
\( Fo \) — Fourier number (dimensionless)

Explanation: This formula accounts for the energy change in a lumped system where internal temperature gradients are negligible, using Biot and Fourier numbers to characterize the heat transfer process.

3. Importance of Internal Energy Calculation

Details: Calculating internal energy changes is crucial for thermal analysis, energy balance studies, and designing thermal systems in various engineering applications including HVAC, materials processing, and energy systems.

4. Using the Calculator

Tips: Enter all parameters with appropriate units. Density, specific heat, and volume must be positive values. Biot and Fourier numbers should be non-negative. Temperature values should be in Kelvin for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a lumped body assumption?
A: The lumped body assumption considers that the temperature within the body is uniform at any given time, valid when Biot number is less than 0.1.

Q2: Why are Biot and Fourier numbers important?
A: Biot number compares internal to external resistance to heat transfer, while Fourier number relates conduction rate to energy storage rate.

Q3: What are typical units for internal energy?
A: Internal energy is typically measured in Joules (J) in the SI system.

Q4: When is this calculation applicable?
A: This calculation applies to systems with negligible internal temperature gradients and constant material properties.

Q5: How does fluid temperature affect the result?
A: The temperature difference between initial and fluid temperatures drives the heat transfer process and directly influences the energy change.