Question

Question 4 2 pts An air compressor, operated at steady state, compresses air from 1 bar 25°C to 8 bar. At the outlet of the compressor, the air temperature is 90°C. The compressor transfers heat to the surroundings at 200kJ for each kg of air passing through the compressor. The average temperature at which the heat is transferred is 50°C. Which of the following values is closest to the specific entropy production of the compressor process? For air, Cp=1.01 kJ/kgk and R=0.286kJ/kgK. Hints: Air can be treated as ideal gas. 0.2238 kJ/kgK 1.01462 kJ/kg 3.0827 kJ/kgK 6.5 kJ/kgk

Answer 1

Answer:

(a) s_gen = 0.2238 kJ/kg.K

Solution:

By entropy balance;

$s_{in} - s_{out}+s_{gen} = \Delta s_{sys}$

$\Rightarrow 0 -\frac{q_{out}}{T}+s_{gen} = c_pln\left ( \frac{T_2}{T_1} \right )- Rln\left ( \frac{P_2}{P_1} \right )$

$\Rightarrow 0 -\frac{200}{(50+273)}+s_{gen} = 1.01ln\left ( \frac{90+273}{25+273} \right )- 0.286ln\left ( \frac{8}{1} \right )$

$\Rightarrow 0 -\frac{200}{323}+s_{gen} = 1.01ln\left ( \frac{363}{298} \right )- 0.286ln\left ( \frac{8}{1} \right )$

$\Rightarrow s_{gen} = 0.2238\;\;kJ/kg.K$

...(Answer)