Temperature of Ideal Gas given its Internal Energy Calculator

✖The 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.ⓘ Internal Energy [U]			+10% -10%
✖The Degree of Freedom of a system is the number of parameters of the system that may vary independently.ⓘ Degree of Freedom [F]			+10% -10%
✖Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight.ⓘ Number of Moles [N_moles]			+10% -10%

✖Temperature of Gas is the measure of hotness or coldness of a gas.ⓘ Temperature of Ideal Gas given its Internal Energy [T_g]

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Formula

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Temperature of Ideal Gas given its Internal Energy

Formula

`"T"_{"g"} = 2*"U"/("F"*"N"_{"moles"}*"[BoltZ]")`

Example

`"1.5E^24K"=2*"121J"/("3"*"4"*"[BoltZ]")`

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Temperature of Ideal Gas given its Internal Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ])
T_g = 2*U/(F*N_moles*[BoltZ])
This formula uses 1 Constants, 4 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Variables Used

Temperature of Gas - (Measured in Kelvin) - Temperature of Gas is the measure of hotness or coldness of a gas.
Internal Energy - (Measured in Joule) - The 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.
Degree of Freedom - The Degree of Freedom of a system is the number of parameters of the system that may vary independently.
Number of Moles - Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight.

STEP 1: Convert Input(s) to Base Unit

Internal Energy: 121 Joule --> 121 Joule No Conversion Required
Degree of Freedom: 3 --> No Conversion Required
Number of Moles: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_g = 2*U/(F*N_moles*[BoltZ]) --> 2*121/(3*4*[BoltZ])

Evaluating ... ...

T_g = 1.46066622855371E+24

STEP 3: Convert Result to Output's Unit

1.46066622855371E+24 Kelvin --> No Conversion Required

FINAL ANSWER

1.46066622855371E+24 ≈ 1.5E+24 Kelvin <-- Temperature of Gas

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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< 8 Ideal Gas Calculators

Isothermal Compression of Ideal Gas

Go Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System)

Molar Internal Energy of Ideal Gas given Boltzmann Constant

Go Internal Energy = (Degree of Freedom*Number of Moles*[BoltZ]*Temperature of Gas)/2

Number of Moles given Internal Energy of Ideal Gas

Go Number of Moles = 2*Internal Energy/(Degree of Freedom*[BoltZ]*Temperature of Gas)

Temperature of Ideal Gas given its Internal Energy

Go Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ])

Degree of Freedom given Molar Internal Energy of Ideal Gas

Go Degree of Freedom = 2*Internal Energy/(Number of Moles*[R]*Temperature of Gas)

Ideal Gas Law for Calculating Volume

Go Ideal Gas Law for Calculating Volume = [R]*Temperature of Gas/Total Pressure of Ideal Gas

Ideal Gas Law for Calculating Pressure

Go Ideal Gas Law for calculating Pressure = [R]*(Temperature of Gas)/Total Volume of System

Molar Internal Energy of Ideal Gas

Go Molar Internal Energy of Ideal gas = (Degree of Freedom*[R]*Temperature of Gas)/2

Temperature of Ideal Gas given its Internal Energy Formula

Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ])
T_g = 2*U/(F*N_moles*[BoltZ])

What is internal energy?

Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale.

How to Calculate Temperature of Ideal Gas given its Internal Energy?

Temperature of Ideal Gas given its Internal Energy calculator uses Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ]) to calculate the Temperature of Gas, The Temperature of Ideal Gas given its Internal Energy formula is a measure of the average translational kinetic energy of the molecules. Temperature of Gas is denoted by T_g symbol.

How to calculate Temperature of Ideal Gas given its Internal Energy using this online calculator? To use this online calculator for Temperature of Ideal Gas given its Internal Energy, enter Internal Energy (U), Degree of Freedom (F) & Number of Moles (N_moles) and hit the calculate button. Here is how the Temperature of Ideal Gas given its Internal Energy calculation can be explained with given input values -> 1.5E+24 = 2*121/(3*4*[BoltZ]).

FAQ

What is Temperature of Ideal Gas given its Internal Energy?

The Temperature of Ideal Gas given its Internal Energy formula is a measure of the average translational kinetic energy of the molecules and is represented as T_g = 2*U/(F*N_moles*[BoltZ]) or Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ]). The 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, The Degree of Freedom of a system is the number of parameters of the system that may vary independently & Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight.

How to calculate Temperature of Ideal Gas given its Internal Energy?

The Temperature of Ideal Gas given its Internal Energy formula is a measure of the average translational kinetic energy of the molecules is calculated using Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ]). To calculate Temperature of Ideal Gas given its Internal Energy, you need Internal Energy (U), Degree of Freedom (F) & Number of Moles (N_moles). With our tool, you need to enter the respective value for Internal Energy, Degree of Freedom & Number of Moles 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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