Help please thank you
1 answer:
You might be interested in
Answer:
a) the heat exchanger area required for the evaporator is 11178.236 m²
b) the required flow rate is 1993630.38 kg/s
Explanation:
Given the data in the question;
Water temperature near the surface = 300 K
temperature at reasonable depths ( cold ) = 280 K
power plant output W' = 2 MW
efficiency η = 3% = 0.03
we know that; efficiency η = W' / Q
we substitute
0.03 = 2 / Q
Q = 2 / 0.03
Q = 66.667 MW = 66.667 × 10⁶ Watt
T = 300 K T
= 292 K
T = 290 K T
= 290 K
Now, Heat transfer in evaporator;
Q = UA( LMTD )
so
LMTD = (ΔT₁ - ΔT₂) / ln( ΔT₁ / ΔT₂ )
first we get ΔT₁ and ΔT₂
ΔT₁ = T - T
= 300 - 290 = 10 K
ΔT₂ = T - T
= 292 - 290 = 2 K
so we substitute into our equation;
LMTD = (10 - 2) / ln( 10 / 2 )
LMTD = 8 / ln( 5 )
LMTD = 8 / 1.6094379
LMTD = 4.97
a) Heat transfer Area will be;
Q = UA( LMTD )
we substitute
66.667 × 10⁶ = 1200 × A × 4.97
66.667 × 10⁶ = 5964 × A
A = (66.667 × 10⁶) / 5964
A = 11178.236 m²
Therefore, the heat exchanger area required for the evaporator is 11178.236 m²
b) Flow rate
we know that;
Q = m'C
(
-
)
specific heat capacity of water Cp = 4.18 (kJ/kg∙°C)
we substitute
66.667 × 10⁶ = m' × 4.18 × ( 300 - 292 )
66.667 × 10⁶ = m' × 33.44
m' = ( 66.667 × 10⁶ ) / 33.44
m' = 1993630.38 kg/s
Therefore, the required flow rate is 1993630.38 kg/s
Answer with Explanation:
The crown will be pure if it's specific gravity is 19.3
Now by definition of specific gravity it is the ratio between the weight of an object to the weight of water of equal volume
Since it is given that the weight of the crown is 11.8 N we need to find it's volume
Now According to Archimedes principle when the crown is immersed into water the water shall exert a force in upwards direction on the crown with a magnitude equaling to weight of the water displaced by the crown
Mathematically this is the difference between the weight of the crown in air and weight when immersed in water
Thus Buoyant force is
Now by Archimedes principle This force equals in magnitude to the weight of water of same volume as of the crown
Thus the specific gravity of the crown equals
As we see that the specific gravity of the crown material is less than that of pure gold hence we conclude that it is impure.