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
Heaterwater · 20 °C60 °CQ = ?

A stream of water flowing at 0.8 kg/s is heated from 20 °C to 60 °C. Find the heat duty Q.

ṁ = 0.8 kg/scp = 4.18 kJ/(kg·K)Tin = 20 °CTout = 60 °C
Q = kW
2.Easy
Heaterethanol · 30 °C80 °CQ = ?

A stream of ethanol flowing at 2 kg/s is heated from 30 °C to 80 °C. Find the heat duty Q.

ṁ = 2 kg/scp = 2.44 kJ/(kg·K)Tin = 30 °CTout = 80 °C
Q = kW
3.Medium
hot sidecold sideglycol mix · 150 °C120 °Cwater · 20 °Ct = ? °C

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

ṁh = 1.5 kg/scp,h = 3.6 kJ/(kg·K)Th: 150 → 120 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)tin = 20 °C
tout = °C
4.Medium
hot sidecold sidelight oil · 170 °C100 °Cwater · 20 °Ct = ? °C

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

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 100 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)tin = 20 °C
tout = °C
5.Hard
hot sidecold sideethanol · 170 °C130 °Cwater · 10 °C45 °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: 170 → 130 °Ct: 10 → 45 °Ccp,c = 4.18 kJ/(kg·K)loss = 5 %
ṁc = kg/s
6.Hard
hot sidecold sidelight oil · 150 °C120 °Cwater · 15 °C40 °C · ṁ = ?15% lost

Hot light oil 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 = 2.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 150 → 120 °Ct: 15 → 40 °Ccp,c = 4.18 kJ/(kg·K)loss = 15 %
ṁc = kg/s

Answer key

  1. 1. Q = 133.8 kW
  2. 2. Q = 244 kW
  3. 3. tout = 32.92 °C
  4. 4. tout = 55.17 °C
  5. 5. ṁc = 1.268 kg/s
  6. 6. ṁc = 1.281 kg/s

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