Question

Water vapor (1.2 kg ) at 0.2 kPa and 30 ∘C is cooled in a constant pressure until condensation begins.

a)Water vapor (1.2 kg ) at 0.2 kPa and 30 ∘C is cooled in a constant pressure until condensation begins.

b)Determine the change of enthalpy (ΔH) treating water as the system.

c)What-if scenario: What would the boundary work transfer be if all the vapor condensed?

d)What-if scenario: What would the change of enthalpy be if all the vapor condensed?

Answer 1

Let us treat the water vapour as polyatomic ideal gas with Specific heat at constant pressure C_p = 4R,

where R is gas constant 8.314 J/ (mole-K)

Number of moles n in 1.2 kg water vapour = 1200/18 = 66.67

(b) change in enthalpy = n C_p$\Delta$T = 66.67$\times$ 4 $\times$ 8.314 $\times$ 30 = 66.512 kJ ..................(1)

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(c) we have $\Delta$ Q = $\Delta$ U+ $\Delta$ W

where $\Delta$ Q is heat transfer ( equals to change in enthalpy), $\Delta$ U is change in internal energy

and $\Delta$ W is work done

$\Delta$u = n C_v$\Delta$T = 66.67 $\times$ 3 $\times$ 8.314 $\times$ 30 = 49.886 kJ

Hence, $\Delta$ W = $\Delta$ Q - $\Delta$ U = ( 66.512 - 49.886 ) kJ = 16.63 kJ ...............(2)

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(d) Change in enthalpy as given in eqn.(1) is when the system attains the state at temperature 0^oC

and starts condensing by absorbing latent heat.

If all 1.2 kg water is completely condensed, then it has absorbed the latent heat

Hence change in enthalpy = 66.512 + 1.2 $\times$ 2260 = 2779 kJ