Question

To 3 significant digits, what is the change of entropy of air in kJ/kgk if the pressure is decreased from 400 to 300 kPa and the temperature is increased from 300 to 900 K? DO NOT ASSUME constant specific heats.

Answer 1

Answer:

The change of entropy is 1.229 kJ/(kg K)

Explanation:

Data

$T_1 = 300 K$

$T_2 = 900 K$

$p_1= 400 kPa$

$p_2= 300 kPa$

$R= 0.287 kJ/(kg K)$ (Individual Gas Constant for air)  

For variable specific heats  

$s(T_2, p_2) - s(T_1, p_1) = s^0(T_2) - s^0(T_1) - R \, ln \frac{p_2}{p_1}$

where $s^0(T)$ is evaluated from table  attached

$s^0(900 K) = 2.84856 kJ/(kg K)$

$s^0(300 K) = 1.70203 kJ/(kg K)$

Replacing in equation

$s(900 K, 300 kPa) - s(300 K, 400 kPa) = 2.84856 kJ/(kg K) - 1.70203 kJ/(kg K) - 0.287 kJ/(kg K) \, ln \frac{300 kPa}{400 kPa}$

$s(900 K, 300 kPa) - s(300 K, 400 kPa) = 1.229 kJ/(kg K)$