Question #242591

Calculate the internal energy and enthalpy of 1kg of air occupying 0.05m ^ 3 at 20bar. If the internal energy is increased by 120kJ as the air is compressed to 50bar, calculate the new volume occupied by 1kg of air. (250.1kJ/kg. 350.1kJ/kg;0.0296m^ 3 )

Expert's answer

. Here, , n = Mair / MWair and MWair ~ 29g/mol. Cp is a polynomial that you can look up in your book or on the NIST website: , where T is in Kelvin and Cp is in J/mol-K. The values of the constants are: . You can integrate this polynomial fairly easily.

But we do not know T1 or T2. Use the ideal gas equation of state to determine

The problem is that T2 is the ONLY unknown in the equation. You could use SOLVER in EXCEL or a more powerful math package to determine a value of T2 that yields a ?U of 120 kJ. Once you know T2, use the ideal gas equation of state to determine

An approximate solution could be obtained if you assume the Cp of air is a constant, say about 1 kJ/kg-K. In this case, ?U = m Cp * (T2-T1). Solving for T2 yields: T2 = T1 + ?U/(m Cp). Plugging in values yields: T2 = 468.81 K = 195.66C.

Finally, V2 = 0.02688 m^3.

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