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trasher [3.6K]
3 years ago
8

Determine the following parameters for the water having quality x=0.7 at 200 kPa:

Engineering
1 answer:
ra1l [238]3 years ago
7 0

Solution :

Given :

Water have quality x = 0.7 (dryness fraction) at around pressure of 200 kPa

The phase diagram is provided below.

a). The phase is a standard mixture.

b). At pressure, p = 200 kPa, T = $T_{saturated}$

   Temperature = 120.21°C

c). Specific volume

  $v_{f}= 0.001061, \ \ v_g=0.88578 \ m^3/kg$

  $v_x=v_f+x(v_g-v_f)$

       $=0.001061+0.7(0.88578-0.001061)$

       $=0.62036 \ m^3/kg$

d). Specific energy (u_x)

    $u_f=504.5 \ kJ/kg, \ \ u_{fg}=2024.6 \ kJ/kg$

   $u_x=504.5 + 0.7(2024.6)$

         $=1921.72 \ kJ/kg$

e). Specific enthalpy $(h_x)$

   At $h_f = 504.71, \ \ h_{fg} = 2201.6$

   h_x=504.71+(0.7\times 2201.6)

        $= 2045.83 \ kJ/kg$

f). Enthalpy at m = 0.5 kg

  $H=mh_x$

       $= 0.5 \times 2045.83$

       = 1022.91 kJ

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Answer:

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Explanation:

To calculate the heat required for the given process Q, we recall the energy balance equation.

Therefore, : Q = Δ U = m (u₂ - u₁) ..................equation (1)

We should note that there are no kinetic or potential energy change so the heat input in the system is converted only to internal energy.

Therefore, we will start the equation with the mass of the water (m) using given the initial percentage quality as x₁ = 0.123 and initial temperature t₁ = 100⁰c , we can them determine the initial specific volume v₁ of the mixture. For the calculation, we will also need the specific volume of liquid vₙ  = 0.001043m³/kg and water vapour (vₐ) = 1.6720m³/kg

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Moving forward, the mass of the vapor can then be calculated using the given volume of tank V = 14 L but before the calculation, we need to convert the volume to from liters to m³.

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Therefore, u₁ = vₐ + x₁ . vₐₙ

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For the final specific internal energy u₂, we first need to calculate the final quality of the mixture x₂ . The tank is rigid meaning the volume does not change and it is also closed meaning the mass does not change.from this, we can conclude the the specific volume also does not change during the process u₁ = u₂. This allows us to use the given final temperature T₂ = 180⁰c to determine the final quality x₂ of the mixture. for the calculation, we will also need the specific volume of liquid vₙ=0.001091m³/kg and vapor vₐ =  0.39248m³/kg

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We now return to equation (1) to plug in the values generated thus far

Q = m (u₂ - u₁)

0. 0677 kg ( 1641.62 kj/kg - 675.76 kj/kg)

Q = 65.388KJ

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