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Temperature of Real Gas given Heat Capacities Calculator

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✖Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change.ⓘ Heat Capacity Constant Pressure [Cp]
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-10%
✖Heat capacity constant volume is the amount of heat energy absorbed/released per unit mass of a substance where the volume does not change.ⓘ Heat Capacity Constant Volume [Cv]
+10%
-10%
✖The isothermal compressibility is the change in volume due to change in pressure at constant temperature.ⓘ Isothermal Compressibility [KT]
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-10%
✖Specific Volume of the body is its volume per unit mass.ⓘ Specific Volume [v]
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-10%
✖Coefficient of thermal expansion describes how the size of an object changes with a change in temperature.ⓘ Coefficient of Thermal Expansion [α]
+10%
-10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature of Real Gas given Heat Capacities [T]
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Formula
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Temperature of Real Gas given Heat Capacities

Formula
`"T" = (("C"_{"p"}-"C"_{"v"})*"K"_{"T"})/("v"*("α"^2))`

Example
`"192954.5K"=(("1001J/(kg*K)"-"718J/(kg*K)")*"75m²/N")/("11m³/kg"*(("0.1K⁻¹")^2))`

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Temperature of Real Gas given Heat Capacities Solution

STEP 0: Pre-Calculation Summary
Formula Used
Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))
T = ((Cp-Cv)*KT)/(v*(α^2))
This formula uses 6 Variables
Variables Used
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Heat Capacity Constant Pressure - (Measured in Joule per Kilogram per K) - Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change.
Heat Capacity Constant Volume - (Measured in Joule per Kilogram per K) - Heat capacity constant volume is the amount of heat energy absorbed/released per unit mass of a substance where the volume does not change.
Isothermal Compressibility - (Measured in Square Meter per Newton) - The isothermal compressibility is the change in volume due to change in pressure at constant temperature.
Specific Volume - (Measured in Cubic Meter per Kilogram) - Specific Volume of the body is its volume per unit mass.
Coefficient of Thermal Expansion - (Measured in 1 Per Kelvin) - Coefficient of thermal expansion describes how the size of an object changes with a change in temperature.
STEP 1: Convert Input(s) to Base Unit
Heat Capacity Constant Pressure: 1001 Joule per Kilogram per K --> 1001 Joule per Kilogram per K No Conversion Required
Heat Capacity Constant Volume: 718 Joule per Kilogram per K --> 718 Joule per Kilogram per K No Conversion Required
Isothermal Compressibility: 75 Square Meter per Newton --> 75 Square Meter per Newton No Conversion Required
Specific Volume: 11 Cubic Meter per Kilogram --> 11 Cubic Meter per Kilogram No Conversion Required
Coefficient of Thermal Expansion: 0.1 1 Per Kelvin --> 0.1 1 Per Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = ((Cp-Cv)*KT)/(v*(α^2)) --> ((1001-718)*75)/(11*(0.1^2))
Evaluating ... ...
T = 192954.545454545
STEP 3: Convert Result to Output's Unit
192954.545454545 Kelvin --> No Conversion Required
FINAL ANSWER
192954.545454545 ≈ 192954.5 Kelvin <-- Temperature
(Calculation completed in 00.020 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Specific Heat Capacity » Temperature of Real Gas given Heat Capacities

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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14 Specific Heat Capacity Calculators

Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure
Go Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility))
Adiabatic Index of Real Gas given Heat Capacity at Constant Volume
Go Adiabatic Index = (((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)+Heat Capacity Constant Volume)/Heat Capacity Constant Volume
Coefficient of Thermal Expansion of Real Gas
Go Coefficient of Thermal Expansion = sqrt(((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*Temperature))
Specific Volume of Real Gas given Heat Capacities
Go Specific Volume = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Temperature*(Coefficient of Thermal Expansion^2))
Temperature of Real Gas given Heat Capacities
Go Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))
Heat Capacity at Constant Pressure of Real Gas
Go Heat Capacity Constant Pressure = ((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)+Heat Capacity Constant Volume
Heat Capacity at Constant Volume of Real Gas
Go Heat Capacity Constant Volume = Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)
Isothermal Compressibility of Real Gas
Go Isothermal Compressibility = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/(Heat Capacity Constant Pressure-Heat Capacity Constant Volume)
Coefficient of Thermal Expansion of Real Gas given Difference between Cp and Cv
Go Coefficient of Thermal Expansion = sqrt((Difference in Heat Capacities*Isothermal Compressibility)/(Specific Volume*Temperature))
Specific Volume of Real Gas given Difference between Cp and Cv
Go Specific Volume = (Difference in Heat Capacities *Isothermal Compressibility)/(Temperature*(Coefficient of Thermal Expansion^2))
Temperature of Real Gas given Difference between Cp and Cv
Go Temperature = (Difference in Heat Capacities*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))
Isothermal Compressibility of Real Gas given Difference between Cp and Cv
Go Isothermal Compressibility = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Difference in Heat Capacities
Difference between Cp and Cv of Real Gas
Go Difference in Heat Capacities = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility
Adiabatic Index of Real Gas
Go Adiabatic Index = Heat Capacity Constant Pressure/Heat Capacity Constant Volume

Temperature of Real Gas given Heat Capacities Formula

Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))
T = ((Cp-Cv)*KT)/(v*(α^2))

What are postulates of Kinetic molecular theory of gas?

1) Actual volume of gas molecules is negligible in comparison to the total volume of the gas.
2) no force of attraction between the gas molecules.
3) Particles of gas are in constant random motion.
4) Particles of gas collide with each other and with the walls of the container. 5)Collisions are perfectly elastic.
6) Different particles of the gas, have different speeds.
7) The average kinetic energy of the gas molecule is directly proportional to the absolute temperature.

How to Calculate Temperature of Real Gas given Heat Capacities?

Temperature of Real Gas given Heat Capacities calculator uses Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2)) to calculate the Temperature, The Temperature of real gas given Heat Capacities is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale. Temperature is denoted by T symbol.

How to calculate Temperature of Real Gas given Heat Capacities using this online calculator? To use this online calculator for Temperature of Real Gas given Heat Capacities, enter Heat Capacity Constant Pressure (Cp), Heat Capacity Constant Volume (Cv), Isothermal Compressibility (KT), Specific Volume (v) & Coefficient of Thermal Expansion (α) and hit the calculate button. Here is how the Temperature of Real Gas given Heat Capacities calculation can be explained with given input values -> 192954.5 = ((1001-718)*75)/(11*(0.1^2)).

FAQ

What is Temperature of Real Gas given Heat Capacities?
The Temperature of real gas given Heat Capacities is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and is represented as T = ((Cp-Cv)*KT)/(v*(α^2)) or Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2)). Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change, Heat capacity constant volume is the amount of heat energy absorbed/released per unit mass of a substance where the volume does not change, The isothermal compressibility is the change in volume due to change in pressure at constant temperature, Specific Volume of the body is its volume per unit mass & Coefficient of thermal expansion describes how the size of an object changes with a change in temperature.
How to calculate Temperature of Real Gas given Heat Capacities?
The Temperature of real gas given Heat Capacities is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale is calculated using Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2)). To calculate Temperature of Real Gas given Heat Capacities, you need Heat Capacity Constant Pressure (Cp), Heat Capacity Constant Volume (Cv), Isothermal Compressibility (KT), Specific Volume (v) & Coefficient of Thermal Expansion (α). With our tool, you need to enter the respective value for Heat Capacity Constant Pressure, Heat Capacity Constant Volume, Isothermal Compressibility, Specific Volume & Coefficient of Thermal Expansion and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Temperature?
In this formula, Temperature uses Heat Capacity Constant Pressure, Heat Capacity Constant Volume, Isothermal Compressibility, Specific Volume & Coefficient of Thermal Expansion. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Temperature = (Difference in Heat Capacities*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))
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