Question

Carbon dioxide initially at 50 kPa, 400 K, undergoes a process in a closed system until its pressure and temperature are 2 MPa and 800 K, respectively. Assuming an ideal gas behaviour, find the entropy change of the carbon dioxide by assuming that the specific heats are constant. For the gas, take Cp = 0.846 kJ/kg.K and R = 0.1889 kJ/kg.K

Answer 1

The entropy change of ideal gas is given by the following equation (https://www.grc.nasa.gov/WWW/K-12/airplane/entropy.html):

$$\Delta S = C_p \ln\dfrac{T_2}{T_1} - R\ln\dfrac{P_2}{P_1}$$

where $T_1 = 400K, P_1 = 50\times 10^3Pa$ are its parameters at the begining of the process and $T_2 = 800K, P_1 = 2\times 10^6Pa$ are parameters at the end of the process. Thus, obtain:

$$\Delta S = 0.846\cdot 10^3 \ln\dfrac{800}{400} - 0.1889\cdot 10^{3}\ln\dfrac{2\cdot 10^6}{50\cdot 10^{3}} = \\ \approx 110.4 J/kg\cdot K$$

Answer. 110.4 J/kg.K.