# GATE Mechanical 2014 Set 2 | Question: 46

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 _______

recategorized 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.

540 points 1 2 8

## Related questions

A pure substance at $8$ $MPa$ and $400^0C$ is having a specific internal energy of $2864$ $kJ/kg$ and a specific volume of $0.03432$ $m^3$/$kg$. Its specific enthalpy (in $kJ/kg$) is _______
One kg of an ideal gas (gas constant $R= 287\: J/kg.K$) undergoes an irreversible process from state-$1$ ($1$ bar, $300 \: K$) to state-$2$ ($2$ bar, $300\: K$). The change in specific entropy $(s_{2} - s_{1})$ of the gas (in $J/kg.K$) in the process is _________.
Work is done on an adiabatic system due to which its velocity changes from $10$ $m/s$ to $20$ $m/s$, elevation increases by $20$ $m$ and temperature increases by $1$ $K$. The mass of the system is $10$ $kg$, $C_v$ = $100$ $J/(kg.K)$ and gravitational ... $kJ$) on the system is _______
Air (ideal gas) enters a perfectly insulated compressor at a temperature of $310\: K$. The pressure ratio of the compressor is $6$. Specific heat at constant pressure for air is $1005\: J/kg . K$ and ratio of specific heats at constant pressure and constant ... the difference in enthalpies of air between the exit and the inlet of the compressor is _________ $kJ/kg$ (round off to nearest integer).
One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: J/kg.K$, the magnitude of work transfer is ________ $kJ$ (round off to $2$ decimal places).