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 · 25 °C50 °CQ = ?

A stream of light oil flowing at 2 kg/s is heated from 25 °C to 50 °C. Find the heat duty Q.

ṁ = 2 kg/scp = 2.1 kJ/(kg·K)Tin = 25 °CTout = 50 °C
Q = kW
2.Easy
Heaterwater · 30 °C95 °CQ = ?

A stream of water flowing at 1.5 kg/s is heated from 30 °C to 95 °C. Find the heat duty Q.

ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tin = 30 °CTout = 95 °C
Q = kW
3.Medium
hot sidecold sidelight oil · 140 °C110 °Cwater · 10 °Ct = ? °C

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

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 140 → 110 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)tin = 10 °C
tout = °C
4.Medium
hot sidecold sideethanol · 170 °C110 °Cwater · 15 °Ct = ? °C

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

ṁh = 2 kg/scp,h = 2.44 kJ/(kg·K)Th: 170 → 110 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)tin = 15 °C
tout = °C
5.Hard
hot sidecold sideethanol · 160 °C100 °Cwater · 10 °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 = 1.5 kg/scp,h = 2.44 kJ/(kg·K)Th: 160 → 100 °Ct: 10 → 85 °Ccp,c = 4.18 kJ/(kg·K)loss = 15 %
ṁc = kg/s
6.Hard
hot sidecold sideglycol mix · 120 °C90 °Cwater · 25 °C75 °C · ṁ = ?15% lost

Hot glycol mix 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 = 1 kg/scp,h = 3.6 kJ/(kg·K)Th: 120 → 90 °Ct: 25 → 75 °Ccp,c = 4.18 kJ/(kg·K)loss = 15 %
ṁc = kg/s

Answer key

  1. 1. Q = 105 kW
  2. 2. Q = 407.5 kW
  3. 3. tout = 13.77 °C
  4. 4. tout = 61.7 °C
  5. 5. ṁc = 0.5954 kg/s
  6. 6. ṁc = 0.4392 kg/s

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