GATE Mechanical 2014 Set 2 | Question: 46

Question

In an ideal Brayton cycle, atmospheric air (ratio of specific heats, $c_p$/$c_v$ = $1.4$, specific heat at constant pressure = $1.005$ $kJ/kg.K$) at $1$ $bar$ and $300$ $K$ is compressed to $8$ $bar$. The maximum temperature in the cycle is limited to $1280$ $K$. If the heat is supplied at the rate of $80$ $MW$, the mass flow rate (in $kg/s$) of air required in the cycle is _______

Answer 1

Ans: 108 kg/s

Explanation:

Given Data –   Cp/Cv = 1.4; Cp=1.005 KJ/KgK; P1= 1 bar, P2=8 bar.; T1=300K, T3=1280K; Qin= 80MW

The Brayton cycle has constant pressure Heat addition and Rejection process. Assuming air to be ideal gas.

$Q=\dot{m}\cdot Cp(T3-T2)$…...(1) and $T2/T1 = (P2/P1)^(\gamma -1)/\gamma$ ...(2)

Using the data given and solving the equations above, we get m=108 kg/s.