In a closed vessel there is a mixture of nitrogen with a mass of 112 g and oxygen with a mass of 128 g. Determine the change in the internal energy of this mixture when it is heated by 40 g Celsius.
To calculate the change in the internal energy of the specified gas mixture after heating, we use the formula: ΔU = UN2 + UO2 = (mN2 / MN2 + mO2 / MO2) * i * R * ΔT / 2.
Constants and variables: mN2 – mass of nitrogen (mN2 = 112 g); MN2 is the molar mass of nitrogen (MN2 = 28 g / mol); mО2 is the mass of oxygen (mО2 = 128 g); MО2 – molar mass of oxygen (MО2 = 32 g / mol); i is the number of degrees of freedom of molecules (the gases taken are diatomic; i = 5); R – universal gas constant (R = 8.31 J / (K * mol)); T is the change in the temperature of the mixture (T = 40 ºС).
Let’s calculate: ΔU = (112/28 + 128/32) * 5 * 8.31 * 40/2 = 6648 J.
Answer: The internal energy of the indicated gas mixture increased by 6648 J.
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