GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 54 of 65

Marks: +1, -0

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^{∘} {C}

with a volume flow rate of

15 {m}^{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=1 {kJ} {/} {kg} {K} ; {R}=0.5 {kJ}{/} {kg} {K})

$37^{∘} {C}$
$53^{∘} {C}$
$32^{∘} {C}$
$76^{∘} {C}$

Validate

Solution:

From ideal gas equation,

{pV}=˙{m} {RT}

100 × 15=˙{m} × 0.5 × 300

⇒ ˙{m}=10 {kg} {\/} {s}

Using SFEE,

˙{m} h_{1}+Q_{m}+Q_{\;\text "out "\;}=˙{m} h_{2}+W_{c v}

⇒ ˙{m} h_{1}+101+(-51)=˙{m} h_{2}

˙{m}(h_{2}-h_{1})=50

Or,

˙{m} C_{p}(T_{2}-T_{1})=50

⇒ 10 × 1(T_{2}-300)=50

Or,

(T_{2}-300)=5

⇒ T_{2}=305 {K}=305-273=32^{∘} {C}

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