How Do You Calculate Boiler Efficiency and Energy Transfer?

[Aaron9890]

Thermodynamics question help?? is this right??

Homework Statement

A boiler is supplied with water at a rate of 0.3 kg/s through a pipe of diameter 50mm

a) calculate the energy per second that must be supplied to the boiler,raising the water temperature to 100C, when the water is supplied at 15C

b) If the input power to the boiler is 3.1GJ/h, Calculate the efficiency of the boiler and heat transfer process


The density of water - 1000kg/m^3
specific heat capacity for water - 4.7kj/kgK
latent heat evaporation for water - 2.26MJj /kg
steam pipe outside diameter - 55mm
steam pipe wall thickness - 2.5mm
modulus of elasticity for steel - 210GPA
coefficient of linear expansion of steel - 18 x 10^-6/C

Homework Equations

Q = MCAO + ML (mass flow rate x heat capacity x change in temp) + (mass flow rate x latent heat for evaporation of water)

Thermal efficiency = Q out / Q in

The Attempt at a Solution

M = 0.3 kg/s
c = 4.7 KJ/kgK in J = 4700J/kgK
AO = 100C - 15C = 85C
L -= 2.26MJ/KgK in J = 2260000J/kgK

so Q = MCAO + ML
Q = (0.3)x(4700)x(85) + (0.3) x (2260000)
Q = 797 850 J/s or 0.79785MJ/s


Thermal Efficency = Qout / Qin
Thermal Efficency = 797.850J / 3100000000J
=? (please help me out on this one)

 

[LawrenceC]

Hint: Watch your units.

 

[Aaron9890]

for the efficiency??

 

[LawrenceC]

Hint: Look at the numeric information given in the problem statement more closely.

 

[rude man]

Hint: how does the 50mm figure in?

 

[Aaron9890]

all the values in the list there are at the bottom of the page i have, they are for a number of questions, i think there are 6 but only some will apply for this question. So i don't have to use them all!

 

[rude man]

all the values in the list there are at the bottom of the page i have, they are for a number of questions, i think there are 6 but only some will apply for this question. So i don't have to use them all!

Good, 'cause you can toss that one out.

 

[Aaron9890]

c = 4.7 KJ/kgK in J = 4700J/kgK
L -= 2.26MJ/KgK in J = 2260000J/kgK

did i transpose on of these wrong

 

[rude man]

Well, there's a question here. Is the water just raised to 100^oC or is it then changed to steam at 100^oC? The question doesn't say. If the former, do you need L? (I suppose 'boiler' does imply steam but who knows ...)

Anyway, like Lawrence told you - watch your units. What should the units of L be, assuming you need L in the first place?