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Time taken to reach given temperature Formula

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Time Elapsed after a particular task is started. Check FAQs

t = \ln (\frac{T f - t f}{T o - t f}) \cdot (\frac{ρ \cdot V T \cdot c}{h \cdot A})

t - Time Elapsed?T_f - Final Temperature?t_f - Fluid Temperature?T_o - Initial Temperature?ρ - Density?V_T - Total Volume?c - Specific Heat?h - Convection Heat Transfer Coefficient?A - Surface Area?

Time taken to reach given temperature Example

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Here is how the Time taken to reach given temperature equation looks like with Values.

Here is how the Time taken to reach given temperature equation looks like with Units.

Here is how the Time taken to reach given temperature equation looks like.

12 = \ln (\frac{20.0021 - 10}{20 - 10}) \cdot (\frac{5.51 \cdot 63 \cdot 120}{0.04 \cdot 18})

12s = \ln (\frac{20.0021K - 10K}{20K - 10K}) \cdot (\frac{5.51kg/m³ \cdot 63m³ \cdot 120J/(kg*K)}{0.04W/m²*K \cdot 18m²})

12 = \ln (\frac{20.0021 - 10}{20 - 10}) \cdot (\frac{5.51 \cdot 63 \cdot 120}{0.04 \cdot 18})

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Home » Physics » Mechanical » Heat and Mass Transfer » Time taken to reach given temperature

Time taken to reach given temperature Solution

Follow our step by step solution on how to calculate Time taken to reach given temperature?

FIRST Step Consider the formula

t = \ln (\frac{T f - t f}{T o - t f}) \cdot (\frac{ρ \cdot V T \cdot c}{h \cdot A})

Next Step Substitute values of Variables

∴

t = \ln (\frac{20.0021K - 10K}{20K - 10K}) \cdot (\frac{5.51kg/m³ \cdot 63m³ \cdot 120J/(kg*K)}{0.04W/m²*K \cdot 18m²})

Next Step Prepare to Evaluate

∴

t = \ln (\frac{20.0021 - 10}{20 - 10}) \cdot (\frac{5.51 \cdot 63 \cdot 120}{0.04 \cdot 18})

Next Step Evaluate

∴

t = 11.9999999164213s

LAST Step Rounding Answer

∴

t = 12s

Time taken to reach given temperature Formula Elements

Variables

Functions

Time Elapsed

Time Elapsed after a particular task is started.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Final Temperature

The Final Temperature is the temperature at which measurements are made in final state.

Symbol: T_f

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Fluid Temperature

Fluid Temperature is the temperature of the fluid surrounding the object.

Symbol: t_f

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Initial Temperature

The Initial Temperature is defined as the measure of heat under initial state or conditions.

Symbol: T_o

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Density

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.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Total Volume

Total Volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.

Symbol: V_T

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Specific Heat

The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.

Symbol: c

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value can be positive or negative.

Convection Heat Transfer Coefficient

Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.

Symbol: h

Measurement: Heat Transfer CoefficientUnit: W/m²*K

Note: Value should be greater than 0.

Surface Area

The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Credits

Created by Ravi Khiyani

Indian Institute of Technology, Madras (IIT Madras), Chennai

Ravi Khiyani has created this Formula and 200+ more formulas!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Formula and 2500+ more formulas!

Other formulas in Transient Heat Conduction category

Go Instantaneous heat transfer rate

Q rate = h \cdot A \cdot (T o - t f) \cdot (\exp (- \frac{h \cdot A \cdot t}{ρ \cdot V T \cdot C o}))

Go Total Heat Transfer during Time Interval

Q = ρ \cdot c \cdot V T \cdot (T o - t f) \cdot (1 - (\exp (- (Bi \cdot Fo))))

How to Evaluate Time taken to reach given temperature?

Time taken to reach given temperature evaluator uses Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total Volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area)) to evaluate the Time Elapsed, The Time taken to reach given temperature formula calculates the time required for a lumped body to reach a certain temperature by using the Temperature-Time relation for the lumped body. Time Elapsed is denoted by t symbol.

How to evaluate Time taken to reach given temperature using this online evaluator? To use this online evaluator for Time taken to reach given temperature, enter Final Temperature (T_f), Fluid Temperature (t_f), Initial Temperature (T_o), Density (ρ), Total Volume (V_T), Specific Heat (c), Convection Heat Transfer Coefficient (h) & Surface Area (A) and hit the calculate button.

FAQs on Time taken to reach given temperature

What is the formula to find Time taken to reach given temperature?

The formula of Time taken to reach given temperature is expressed as Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total Volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area)). Here is an example- 30699.5 = ln((20.002074366-10)/(20-10))*((5.51*63*120)/(0.04*18)).

How to calculate Time taken to reach given temperature?

With Final Temperature (T_f), Fluid Temperature (t_f), Initial Temperature (T_o), Density (ρ), Total Volume (V_T), Specific Heat (c), Convection Heat Transfer Coefficient (h) & Surface Area (A) we can find Time taken to reach given temperature using the formula - Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total Volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area)). This formula also uses Natural Logarithm (ln) function(s).

Can the Time taken to reach given temperature be negative?

No, the Time taken to reach given temperature, measured in Time cannot be negative.

Which unit is used to measure Time taken to reach given temperature?

Time taken to reach given temperature is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time taken to reach given temperature can be measured.

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Time taken to reach given temperature Formula

Time taken to reach given temperature Example

Time taken to reach given temperature Solution

Time taken to reach given temperature Formula Elements

Credits

Other formulas in Transient Heat Conduction category

How to Evaluate Time taken to reach given temperature?

FAQs on Time taken to reach given temperature

Variable Name