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Standard XII

Physics

Energy

A calorically...

Question

A calorically perfect gas (specific heat at constant pressure 1000 J/kgK) enters and leaves a gas turbine with the same velocity. The temperature of the gas at turbine entry and exit are 1100 K and 400 K, respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is

6.14

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7.00

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7.50

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8.00

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Solution

The correct option is B 7.00
(b)
$c_{p} = 1 k J / k g - K$

$V_{i} = V_{e}$ (Inlet and exit velocity same)
$W_{c v} = 4.6 M W = 4.6 \times 10^{3} k W$
Applying SFEE,
$m (h_{i} + \frac{1}{2} v_{i}^{2} + g z_{i} + Q = m (h_{e} + \frac{1}{2} v_{e}^{2} + g z_{e} + W_{c v}$
$m [c_{p} (T_{i} - T_{e})] + Q = W_{c . v .}$ $(L e t z_{i} = z_{e})$
$m [1 \times (1100 - 400)] + (- 300) = 4.6 \times 10^{3}$
$\Rightarrow$ $m = 7 k g / s$

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The correct option is B 7.00(b) cp=1kJ/kg−K Vi=Ve (Inlet and exit velocity same) Wcv=4.6MW=4.6×103kW Applying SFEE, m(hi+12v2i+gzi+Q=m(he+12v2e+gze+Wcv m[cp(Ti−Te)]+Q=Wc.v. (Letzi=ze) m[1×(1100−400)]+(−300)=4.6×103 ⇒ m=7kg/s