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

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

Step-by-step 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 (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 (300 kPa)/(400 kPa)`

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