Question

Carbon dioxide (CO2) expands isothermally at steady state with no irreversibilities through a turbine from 10 bar, 500 K to 2 bar. Assuming the ideal gas model and neglecting kinetic and potential energy effects, determine the heat transfer and work, each in kJ per kg of carbon dioxide flowing.

Answer 1

Answer:

The answer to the question above is = 152.02 KJ/Kg

Explanation:

Given:

Temperature at first state, (T$1$)= 500k

Temperature at second state, (T$2$)= 500k

The above explains an isothermal process as a thermodynamic process,in which the temperature of the system remains constant

Pressure at first state, (p$1$) = 10 bar

Pressure at second state, (p$2$) = 2 bar

The heat transfer=

Qrev/m= T x [s(T$2$) - s(T$1$) - R ㏑ (p$2$ ÷ p$1$)]

Isothermal means the temperature does not change, while Expansion means the volume has increased.

For the internal isothermal process:

Qrev/m=  T x [- R ㏑ (p$2$ ÷ p$1$)]

= 500 x  - (8.314 ÷ 44.01) x In (2 ÷ 10) = 152.02 KJ/Kg

Energy equation at turbine is for the internally reversible isothermal process is:

Q-w = m [( (V$2$²- V$1$²) ÷ 2) + g ( Z$2$ - Z$1$)]

where w= the most efficient work possible in  J

Neglecting the effect of both potential and kinetic energy

(w/ m) = Qrev/ m

= 152.02 KJ/Kg