How to find the initial temperature of gas

How to find the initial temperature of gas

Often during any technological process or at the solution of tasks from a course of thermodynamics there is a need to answer a question: what was the reference temperature of the mix of gases which was under certain conditions (volume, pressure, etc.)


1. Let's assume, such conditions are set. Mix of three gases: hydrogen, carbon dioxide and oxygen, originally occupied a vessel of 22, 4 liters. The mass of hydrogen was 8 g, the mass of carbon dioxide – 22 g, and oxygen – 48 g. At the same time the partial pressure of hydrogen was leveled approximately 4.05*10^5 by Pa, carbon dioxide – 5.06*10^4 in Pa, and oxygen, respectively – 3.04*10^5 in Pa. It is required to determine the initial temperature of this gas mix.

2. First of all remember the law Daltona saying: the general pressure of the mix of gases which is in some volume is equal to the sum of partial pressure of each of components of this mix. Put sizes known to you: 4.05*10^5 + 0.506*10^5 + 3.04*10^5 = 7.596*10^5 Pa. For simplification of calculations accept the rounded value: 7.6*10^5 Pa. Such is pressure of gas mix.

3. Now you will be come to the rescue by the universal equation of Mendeleyev-Klapeyrona describing a condition of ideal gas. Certainly, any of components of your mix is not ideal gas, but it can quite be used in calculations – the error will be very small. This equation registers in such form: PV = MRT/m where P is gas pressure, V – its volume, R – a universal gas constant, M – the actual mass of gas, m – its molar weight.

4. But you have mix of gases. How to be in this case? It is necessary to transform only a little Mendeleyev-Klapeyrona's equation, having written down it in such look: PV = (M1/m1 + M2/m2 + M3/m3) RT.

5. It is easily possible to understand that if the quantity of components of gas mix was equal 4, 5, 6, etc., the equation would be transformed absolutely the same way. Therefore, the required reference temperature of gas mix is calculated on a formula: T = PV / (M1/m1 + M2/m2 + M3/m3) R.

6. Having substituted values known to you (taking into account that size R is equal to 8.31) in this formula, and having made calculations, you receive: 7.6*10^5 * 0.0224 / (8.31 * 7.5) = 17024/62.325 = 273.15. This value of temperature is expressed, certainly, in degrees Kelvin. That is it turns out that originally gas mix contained at a temperature, equal 0 degrees on Celsius scale. The task is solved.

Author: «MirrorInfo» Dream Team