ChemicalEnergy BalanceseasyFE ExamCoursework

Duty for Sensible Heating of Water

Water flows at $\dot m = 2.0\ \text{kg/s}$ and is heated from $20^\circ\text{C}$ to $60^\circ\text{C}$ with no phase change.

Take $c_p = 4.18\ \text{kJ/kg·K}$ .

Find the required heat duty.

Given

m	2 kg/s	Mass flow rate
T1	20 degC	Inlet temperature
T2	60 degC	Outlet temperature
cp	4.18 kJ/kg*K	Specific heat

Hint 1

There is no phase change, so only sensible heat is involved.

Hint 2

Q = ṁc_pΔT.

Hint 3

A temperature difference is the same number in °C and K.

Worked solution — try the problem first

For sensible heating with no phase change:

$\dot Q = \dot m c_p \Delta T = 2.0 \times 4.18 \times (60 - 20)$

$= 2.0 \times 4.18 \times 40 = 334.4\ \text{kW}$

$\boxed{\dot Q = 334.4\ \text{kW}}$

Celsius is fine here. A temperature difference is numerically identical in °C and K, so no conversion is needed. That is only true for differences — an absolute temperature (in the ideal gas law, say, or a radiation calculation) must be in kelvin.

No latent heat. Since the water stays liquid throughout, only sensible heat is involved. Had it been vaporised, the far larger $\dot m h_{fg}$ term would dominate — around 4500 kW for this flow.

Concepts:Energy balancesSensible heatSpecific heat capacity

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