In a gas turbine, hot combustion products with the specific heats $c_{p} = 0.98 k J / k g K$ and $c_{v} = 0.7538 k J / k g K$ enters the turnine at $20 b a r$ , $1500 K$ and exists are $1 b a r$ . The isentropic efficiency of hte turbine is $0.9$ . The work developed by the truine per $k g$ of gas flow is

689.64 k J / k g

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794.66 k J / k g

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1009.72 k J / k g

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1312.00 k J / k g

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Solution

The correct option is A $689.64 k J / k g$

Given data:
$c_{p} = 0.98 k J / k g K; c_{v} = 0.7538 k J / k g K$
$p_{1} = 20 b a r; T_{1} = 1500 K; p_{2} = 1 b a r$
$η_{i s e n} = 0.94$
$γ = \frac{c_{p}}{c_{v}} = \frac{0.98}{0.7538} = 1.3$
For process $1 - 2 s$
$\frac{T_{1}}{T_{2 s}} = {(\frac{p_{1}}{p_{2}})}^{\frac{γ - 1}{γ}}$
$\frac{1500}{T_{2 s}} = {(\frac{20}{1})}^{\frac{1.3 - 1}{1.3}} = (20)^{0.2307} = 1.996$
or $T_{2 s} = 751.50 K$
$η_{i s e n} = \frac{T_{1} - T_{2}}{T_{1} - T_{2 s}}$
$0.94 = \frac{1500 - T_{2}}{1500 - 751.50} = \frac{1500 - T_{2}}{748.5}$
or $1500 - T_{2} = 0.94 \times 748.5 = 703.59$
or $T_{2} = 796.41 K$
Work developed by th turbine per $k g$ of gas,
$w = c_{p} (T_{1} - T - 2)$
$= 0.98 (1500 - 796.41)$
$= 689.51 k J / k g$

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In a gas turbine, hot combustion products with the specific heats cp=0.98kJ/kgK and cv=0.7538kJ/kgK enters the turnine at 20bar, 1500K and exists are 1bar. The isentropic efficiency of hte turbine is 0.9. The work developed by the truine per kg of gas flow is