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Phase Change

In a steam po...

Question

In a steam power plant, superheated steam at $10 M O a$ and $500^{o} C$ , is expanded isentropically in a turbine untiil it becomes a saturated vapour. it is then reheated at constant pressure to $500^{o} C$ . The steam is next expanded isentropically in another trubine until it reaches the condenser pressure of $20 k P a$ . Relevant properties of steam are given in the following two tables. The work done by both the turbines together is
$k J / k g$ (roundoff to the nearest integer).
Superheated Steam Table:

Presure, $p$
$(M P a)$ Temp, $p$
$(^{o} C)$ Enthalpy, $h$
$(k J / k g)$ Entropy, $s$
$(k J . k g . K)$

$10$ $500$ $3373.6$ $6.5965$

$1$ $500$ $3478.4$ $7.7621$

Saturated Steam Table:

1512.95

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Solution

The correct option is A 1512.95
Given data:
at $10 M P a, 500^{o} C, h_{1} = 3373.6 k J / k g$
at $1 M P a, 500^{o} C, h_{3} = 3478.4, k J / k g$
$s_{3} = 7.7621 k J / k g K$
at $1 M P a, h_{2} = h_{g} = 2778.1, k J / k g$

$s_{3} = s_{4} = [s_{f} + x (x_{g} - s_{f})] @ 20 k P a$
$s_{3} = 7.7621$
$= 0.319 + x + (7.9085 - 0.8319)$
$x_{4} = 0.9793$
at $20 k P a, h_{4} = h_{f} + x_{4} \times (h_{g} - h_{f})$
$2560.91 k J / k g$
workdone by turbine,
$W_{T} = (h_{1} - h_{2}) + (h_{3} = h_{4})$
$= 1512.95 k J / k g$

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Presure, $p$ $(M P a)$	Temp, $p$ $(^{o} C)$	Enthalpy, $h$ $(k J / k g)$	Entropy, $s$ $(k J . k g . K)$
$10$	$500$	$3373.6$	$6.5965$
$1$	$500$	$3478.4$	$7.7621$