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 · 10 °C40 °CQ = ?

A stream of light oil flowing at 5 kg/s is heated from 10 °C to 40 °C. Find the heat duty Q.

ṁ = 5 kg/scp = 2.1 kJ/(kg·K)Tin = 10 °CTout = 40 °C
Q = kW
2.Easy
Heaterlight oil · 40 °C90 °CQ = ?

A stream of light oil flowing at 0.8 kg/s is heated from 40 °C to 90 °C. Find the heat duty Q.

ṁ = 0.8 kg/scp = 2.1 kJ/(kg·K)Tin = 40 °CTout = 90 °C
Q = kW
3.Medium
hot sidecold sideethanol · 180 °C80 °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 = 0.5 kg/scp,h = 2.44 kJ/(kg·K)Th: 180 → 80 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)tin = 20 °C
tout = °C
4.Medium
hot sidecold sidelight oil · 180 °C140 °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 = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 140 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)tin = 10 °C
tout = °C
5.Hard
hot sidecold sidelight oil · 120 °C90 °Cwater · 15 °C90 °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 = 3 kg/scp,h = 2.1 kJ/(kg·K)Th: 120 → 90 °Ct: 15 → 90 °Ccp,c = 4.18 kJ/(kg·K)loss = 15 %
ṁc = kg/s
6.Hard
hot sidecold sideethanol · 180 °C130 °Cwater · 20 °C60 °C · ṁ = ?10% lost

Hot ethanol 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 = 3 kg/scp,h = 2.44 kJ/(kg·K)Th: 180 → 130 °Ct: 20 → 60 °Ccp,c = 4.18 kJ/(kg·K)loss = 10 %
ṁc = kg/s

Answer key

  1. 1. Q = 315 kW
  2. 2. Q = 84 kW
  3. 3. tout = 29.73 °C
  4. 4. tout = 20.05 °C
  5. 5. ṁc = 0.5124 kg/s
  6. 6. ṁc = 1.97 kg/s

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