Question

Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800°C, and a pressure of 1.50 MPa. It

expands adiabatically as it pushes on the turbine blades and exits at a pressure of 300 kPa.

(a) Calculate its temperature at the time of exit. [5]

(b) Calculate the (maximum) power output of the turning turbine. [5]

(c) The turbine is one component of a model closed-cycle gas turbine engine. Calculate the maximum

efficiency of the engine.

Answer 1

Solution.

$T_i=1073K;$

$P_i=1.50\sdot10^6Pa;$

$P_f=3\sdot 10^5Pa;$

$v=80.0kg/min;$

$a)(\dfrac{P_fV_f}{T_f})^\gamma=(\dfrac{P_iV_i}{T_i})^\gamma;$

$T_f=T_i(\dfrac{P_f}{P_i})^{(\gamma-1)/\gamma};$

$\gamma=\dfrac{5}{3}$ for Argon,

$T_f=1073K\sdot(\dfrac{3\sdot10^5Pa}{1.50\sdot 10^6Pa})^{0.4}=564K;$

$b) \Delta E_{int}=nC_V\Delta T=Q-W_{eng}=0-W_{eng}\implies W_{eng}=-nC_v\Delta T;$

$P=\dfrac{W_{eng}}{t}=\dfrac{-nC_V\Delta T}{t};$

$P=2.12\sdot 10^5W;$

$c)e_c=1-\dfrac{T_f}{T_i}=1-\dfrac{564K}{1073K}=0.475$ or $47.5\%;$

Answer: $a) T_f=564K;$

$b)P=2.12\sdot10^5W;$

$c) e_c=47.5\%.$