Energy balance worksheet with answers

Free printable Energy balance worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Heaterethanol · 30 °C85 °CQ = ?

A stream of ethanol flowing at 3 kg/s is heated from 30 °C to 85 °C. Find the heat duty Q.

ṁ = 3 kg/scp = 2.44 kJ/(kg·K)Tin = 30 °CTout = 85 °C
Q = kW
2.Easy
Heaterethanol · 15 °C80 °CQ = ?

A stream of ethanol flowing at 1.5 kg/s is heated from 15 °C to 80 °C. Find the heat duty Q.

ṁ = 1.5 kg/scp = 2.44 kJ/(kg·K)Tin = 15 °CTout = 80 °C
Q = kW
3.Medium
hot sidecold sideethanol · 140 °C80 °Cwater · 10 °Ct = ? °C

Hot ethanol cools water in a counter-flow heat exchanger with no heat loss. Find the water outlet temperature tout.

ṁh = 1.5 kg/scp,h = 2.44 kJ/(kg·K)Th: 140 → 80 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)tin = 10 °C
tout = °C
4.Medium
hot sidecold sideglycol mix · 160 °C120 °Cwater · 15 °Ct = ? °C

Hot glycol mix cools water in a counter-flow heat exchanger with no heat loss. Find the water outlet temperature tout.

ṁh = 0.5 kg/scp,h = 3.6 kJ/(kg·K)Th: 160 → 120 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)tin = 15 °C
tout = °C
5.Hard
hot sidecold sideethanol · 180 °C90 °Cwater · 25 °C55 °C · ṁ = ?5% lost

Hot ethanol heats water in an exchanger that loses 5% of the heat released by the hot stream to the surroundings. Find the water flow rate ṁc needed.

ṁh = 1 kg/scp,h = 2.44 kJ/(kg·K)Th: 180 → 90 °Ct: 25 → 55 °Ccp,c = 4.18 kJ/(kg·K)loss = 5 %
ṁc = kg/s
6.Hard
hot sidecold sideethanol · 150 °C70 °Cwater · 25 °C85 °C · ṁ = ?15% lost

Hot ethanol heats water in an exchanger that loses 15% of the heat released by the hot stream to the surroundings. Find the water flow rate ṁc needed.

ṁh = 3 kg/scp,h = 2.44 kJ/(kg·K)Th: 150 → 70 °Ct: 25 → 85 °Ccp,c = 4.18 kJ/(kg·K)loss = 15 %
ṁc = kg/s

Answer key

  1. 1. Q = 402.6 kW
  2. 2. Q = 237.9 kW
  3. 3. tout = 62.54 °C
  4. 4. tout = 26.48 °C
  5. 5. ṁc = 1.664 kg/s
  6. 6. ṁc = 1.985 kg/s

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