Answer to Question #276478 in Molecular Physics | Thermodynamics for Jack lakos

Question

If it is sufficient to express the specific heat as a function of temperature with Cp=a+bT, choose one of the chemicals in the list below and calculate the increase in the internal energy of the unit mass from 300K at 150kPa to 500K at constant pressure by deriving the relevant relation. How many errors (%) would have been made if the fixed Cv value were taken?

Answer 1

Solution;

$\Delta u=mc_p(T_2-T_1)$

Take the gas as Oxygen;

$a=25.48$

$b=1.520×10^{-2}$

Hence;

$\Delta u=\int_{T_1}^{T_2}c_p(T)dT$

$\Delta u=\int_{300}^{500}(25.48+0.01520T)dT$

$\Delta u=6312J$