Change in Internal energy of Lumped body Calculator

✖The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.ⓘ Density [ρ]			+10% -10%
✖The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.ⓘ Specific Heat [c]			+10% -10%
✖Total Volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Total Volume [V_T]			+10% -10%
✖The Initial Temperature is defined as the measure of heat under initial state or conditions.ⓘ Initial Temperature [T_o]			+10% -10%
✖Fluid Temperature is the temperature of the fluid surrounding the object.ⓘ Fluid Temperature [t_f]			+10% -10%
✖Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.ⓘ Biot Number [Bi]			+10% -10%
✖Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter.ⓘ Fourier Number [Fo]			+10% -10%

✖The Change in Internal Energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state.ⓘ Change in Internal energy of Lumped body [ΔU]

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Change in Internal energy of Lumped body Solution

STEP 0: Pre-Calculation Summary

Formula Used

Change in Internal Energy = Density*Specific Heat*Total Volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))
ΔU = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo))))
This formula uses 1 Functions, 8 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Change in Internal Energy - (Measured in Joule) - The Change in Internal Energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
Specific Heat - (Measured in Joule per Kilogram per K) - The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.
Total Volume - (Measured in Cubic Meter) - Total Volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.
Initial Temperature - (Measured in Kelvin) - The Initial Temperature is defined as the measure of heat under initial state or conditions.
Fluid Temperature - (Measured in Kelvin) - Fluid Temperature is the temperature of the fluid surrounding the object.
Biot Number - Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.
Fourier Number - Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter.

STEP 1: Convert Input(s) to Base Unit

Density: 5.51 Kilogram per Cubic Meter --> 5.51 Kilogram per Cubic Meter No Conversion Required
Specific Heat: 120 Joule per Kilogram per K --> 120 Joule per Kilogram per K No Conversion Required
Total Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Initial Temperature: 20 Kelvin --> 20 Kelvin No Conversion Required
Fluid Temperature: 10 Kelvin --> 10 Kelvin No Conversion Required
Biot Number: 0.012444 --> No Conversion Required
Fourier Number: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔU = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo)))) --> 5.51*120*63*(20-10)*(1-(exp(-(0.012444*0.5))))

Evaluating ... ...

ΔU = 2583.76500357691

STEP 3: Convert Result to Output's Unit

2583.76500357691 Joule --> No Conversion Required

FINAL ANSWER

2583.76500357691 ≈ 2583.765 Joule <-- Change in Internal Energy

(Calculation completed in 00.004 seconds)

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< Transient Heat Conduction Calculators

Instantaneous heat transfer rate

LaTeX Go Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total Volume*Specific Heat Capacity)))

Total Heat Transfer during Time Interval

LaTeX Go Heat Transfer = Density*Specific Heat*Total Volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))

Power on exponential of temperature-time relation

LaTeX Go Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total Volume*Specific Heat Capacity)

Time Constant in unsteady state heat transfer

LaTeX Go Time Constant = (Density*Specific Heat Capacity*Total Volume)/(Convection Heat Transfer Coefficient*Surface Area)

Change in Internal energy of Lumped body Formula

LaTeX Go

Change in Internal Energy = Density*Specific Heat*Total Volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))
ΔU = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo))))

What is a Lumped body?

In heat transfer analysis, some bodies whose interior temperature remains essentially uniform at any time during a heat transfer process is called lumped body. The temperature of such bodies can be taken to be a function of time only.

How to Calculate Change in Internal energy of Lumped body?

Change in Internal energy of Lumped body calculator uses Change in Internal Energy = Density*Specific Heat*Total Volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number)))) to calculate the Change in Internal Energy, The Change in Internal energy of Lumped body formula calculates the change in internal energy which is equal to the rate of heat transfer through the body for a time interval. Change in Internal Energy is denoted by ΔU symbol.

How to calculate Change in Internal energy of Lumped body using this online calculator? To use this online calculator for Change in Internal energy of Lumped body, enter Density (ρ), Specific Heat (c), Total Volume (V_T), Initial Temperature (T_o), Fluid Temperature (t_f), Biot Number (Bi) & Fourier Number (Fo) and hit the calculate button. Here is how the Change in Internal energy of Lumped body calculation can be explained with given input values -> 2583.765 = 5.51*120*63*(20-10)*(1-(exp(-(0.012444*0.5)))).

FAQ

What is Change in Internal energy of Lumped body?

The Change in Internal energy of Lumped body formula calculates the change in internal energy which is equal to the rate of heat transfer through the body for a time interval and is represented as ΔU = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo)))) or Change in Internal Energy = Density*Specific Heat*Total Volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number)))). The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius, Total Volume is the overall amount of space that a substance or object occupies or that is enclosed within a container, The Initial Temperature is defined as the measure of heat under initial state or conditions, Fluid Temperature is the temperature of the fluid surrounding the object, Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance & Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter.

How to calculate Change in Internal energy of Lumped body?

The Change in Internal energy of Lumped body formula calculates the change in internal energy which is equal to the rate of heat transfer through the body for a time interval is calculated using Change in Internal Energy = Density*Specific Heat*Total Volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number)))). To calculate Change in Internal energy of Lumped body, you need Density (ρ), Specific Heat (c), Total Volume (V_T), Initial Temperature (T_o), Fluid Temperature (t_f), Biot Number (Bi) & Fourier Number (Fo). With our tool, you need to enter the respective value for Density, Specific Heat, Total Volume, Initial Temperature, Fluid Temperature, Biot Number & Fourier Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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