Question

A gas is heated in a duct as it flows over a resistance heater. Consider a 101 kw electric heating system. The gas enters the heating section of the duct at 100 kPa and ${27}^{0}C$ with a volume flow rate of $15m^3/s$. If heat is lost from the gas in the duct to the surroundings at a rate of 51 kW, the exit temperature of the gas is (Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant specific heat; $C_p=1kJ/kgK;R=0.5kJ/kgK)$

• A. ${32}^{0}C$
• B. ${37}^{0}C$
• C. ${76}^{0}C$
• D. ${53}^{0}C$

Answer 1

The correct option is A ${32}^{0}C$


Since it is given an ideal gas
and. $c_p=1kJ/kgK$
$R=0.5kJ/kgK$

at inlet $P_1{\dot{V}}_1=\dot{m}R{T}_1$
$\dot{m}=\frac{P_1{\dot{V}}_1}{R{T}_1}=\frac{100\times 15}{0.5\times 300}=10kg/s$

Using SFEE
$\dot{m}{h}_1+Q=\dot{m}{h}_2+W$
$h_1+\frac{Q}{\dot{m}}=h_2+\frac{W}{\dot{m}}$
$c_p{T}_1-\left[\frac{51}{10}\right]=c_p{T}_2-\frac{101}{10}$
$(T_2-T_1)c_p=\frac{101-51}{10}=5$
$T_2-T_1=\frac{5}{c_p}=5k$
$T_2=300+5=305kor{32}^{0}C$