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Electrical power plants and ships commonly use steam to drive turbines, producing mechanical energy from the pressure of the system. The rotating turbine is connected to a generator that produces electricity. Steam enters a turbine at a high temperature and pressure and exits, still a gas, at a lower temperature and pressure. Determine the final pressure of steam that is converted from 10.0kL at 600kPa and 150C to 18.0kL at 110C.
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Assuming steam, H2O(g), behaves like
an ideal gas, and no gas is lost to
surroundings, there are two states 1&2,
that form the combined gas law:
(P1 x V1)/T1 = (P2 x V2)/T2
where,
P1 = 600kPa
V1 = 10.0kL
T1 = 150ºC + 273.15 = 423.15 K
V2 = 18.0kL
T2 = 110ºC + 273.15 = 383.15 K
(temps. must be in Kelvin, while
others must be in same units)
Solving for P2:
P2 = (P1 x V1 x T2)/(V2 x T1)
Substituting numbers:
P2 = (600kPa x 10.0kL x 383.15 K)/(18.0kL x 423.15 K)
= (600kPa x 10.0 x 383.15)/(18.0 x 423.15)
= 301.824 kPa
*** Answer: 302 kPa ***
(at 3 sig. figs.)