Calculate the Mass of Steam / Enthelpy

[sci0x]

Homework Statement

Dry saturated steam at 3 bar g is used to heat a CIP detergent storage tank from cold via a plate heat exchanger. Calculate mass of steam required:

Initial detergent temp: 10 deg C
Final detergent temp: 80 deg C
Detergent Vol: 20 hl
Detergent density (assume constant): 1020 kg m-3
Specific heat capacity of detergent = 4.13 kj kg-1 K-1
Enthalpy of dry saturated steam at 3 bar gauge = 2738 kJ kg-1
Enthalpy of water at 3 bar gauge = 603 kj kg-1
Effeciency of heat exchange system = 95%

Relevant Equations

Q = MCdT

Detergent:
Volume = 20hl = 2000L
1L = 10^-3 m3
2000L = 2m3

Density: 1020 kgm-3
Mass Detergent: (2)(1020) = 2040 kg

Detergent heat gain = (2040)(4.13)(80-10)
= 589,764 kJ

Detergent heat gain = steam heat loss
589,764 = m(2738-603)(100-0)
Mass Steam = 2.76 kg
95% effeciency = 2.91 kg

The expected answer on the past exam paper was 291 kg.
Please tell me where I am going wrong here.

 

[etotheipi]

Detergent heat gain = steam heat loss
589,764 = m(2738-603)(100-0)

I'm not sure why you've multiplied by 100 here. The enthalpy is given per unit mass. Simply multiplying the change in enthalpy per unit mass by the mass should give you your change in internal energy (or, since no work is done, heat), assuming that pressure and volume stay constant.

It's assumed that the steam condenses but loses no further heat due to cooling (i.e. no further $mc\Delta T$ losses).

 

[sci0x]

Great thanks