It is desired to compress the steam from 100 kPa to 5000 kPa isothermally at 500 °C. During thisprocess the thermodynamic properties of steam might change. If steam behaves ideally at its initialconditions, estimate the fugacity of the steam during this compression process.

Answered: It is desired to compress the steam…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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It is desired to compress the steam from 100 kPa to 5000 kPa isothermally at 500 °C. During this
process the thermodynamic properties of steam might change. If steam behaves ideally at its initial
conditions, estimate the fugacity of the steam during this compression process.

Expert Solution

Step 1

Given data: Initial condition: $T_{1} = 500 ° C = 773 K, P_{1} = 100 k P a$

After isothermal compression, final state: $T_{2} = T_{1} = 773 K, P_{2} = 5000 k P a$

It is also given that the initial condition of steam is ideal. So, fugacity of steam at state 1, $f_{1} = P_{1} = 100 k P a$

From the definition of fugacity:

Chemical potential = $∆ G = (G_{2} - G_{1}) = R T \times \ln (\frac{f_{2}}{f_{1}})$ -------------------------------------- (1)

where G = Gibbs Free energy = (H-TS)

$R$ = Universal gas constant = $8.314 (J / m o l . K)$

Step 2

For state 1: from steam tables at $T_{1} = 500 ° C = 773 K, P_{1} = 100 k P a$ : $H_{1} = 3488.7 (k J / k g), S_{1} = 8.8362 (k J / k g . K)$

So, $G_{1} = (H_{1} - T_{1} S_{1}) = (3488.7 - 773 \times 8.8362)$

$\Rightarrow G_{1} = - 3341.683 (k J / k g) = - 3341.683 (J / g) \times 18 (g / m o l)$ ------------------ $(∵ M_{w a t e r} = 18 (g / m o l))$

$\Rightarrow G_{1} = - 60150.29 (J / m o l)$

Now for state 2: from steam tables at : $T_{2} = T_{1} = 773 K, P_{2} = 5000 k P a$ : $H_{2} = 3434.7 (k J / k g), S_{2} = 6.9781 (k J / k g . K)$

So, $G_{2} = (H_{2} - T_{2} S_{2}) = (3434.7 - 773 \times 6.9781)$

$\Rightarrow G_{2} = - 1959.37 (k J / k g) = - 1959.37 (J / g) \times 18 (g / m o l)$

$\Rightarrow G_{2} = - 35268.68 (J / m o l)$

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It is desired to compress the steam from 100 kPa to 5000 kPa isothermally at 500 °C. During this process the thermodynamic properties of steam might change. If steam behaves ideally at its initial conditions, estimate the fugacity of the steam during this compression process.