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
Heaterlight oil · 30 °C90 °CQ = ?

A stream of light oil flowing at 1 kg/s is heated from 30 °C to 90 °C. Find the heat duty Q.

ṁ = 1 kg/scp = 2.1 kJ/(kg·K)Tin = 30 °CTout = 90 °C
Q = kW
2.Easy
Heaterwater · 15 °C55 °CQ = ?

A stream of water flowing at 0.5 kg/s is heated from 15 °C to 55 °C. Find the heat duty Q.

ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tin = 15 °CTout = 55 °C
Q = kW
3.Medium
hot sidecold sidelight oil · 180 °C90 °Cwater · 30 °Ct = ? °C

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

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 90 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)tin = 30 °C
tout = °C
4.Medium
hot sidecold sideethanol · 140 °C70 °Cwater · 20 °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 → 70 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)tin = 20 °C
tout = °C
5.Hard
hot sidecold sideethanol · 180 °C110 °Cwater · 25 °C80 °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 = 2 kg/scp,h = 2.44 kJ/(kg·K)Th: 180 → 110 °Ct: 25 → 80 °Ccp,c = 4.18 kJ/(kg·K)loss = 5 %
ṁc = kg/s
6.Hard
hot sidecold sideglycol mix · 150 °C90 °Cwater · 30 °C55 °C · ṁ = ?10% lost

Hot glycol mix heats water in an exchanger that loses 10% of the heat released by the hot stream to the surroundings. Find the water flow rate ṁc needed.

ṁh = 1.5 kg/scp,h = 3.6 kJ/(kg·K)Th: 150 → 90 °Ct: 30 → 55 °Ccp,c = 4.18 kJ/(kg·K)loss = 10 %
ṁc = kg/s

Answer key

  1. 1. Q = 126 kW
  2. 2. Q = 83.6 kW
  3. 3. tout = 120.4 °C
  4. 4. tout = 81.29 °C
  5. 5. ṁc = 1.412 kg/s
  6. 6. ṁc = 2.79 kg/s

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