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GRADE 8 PRACTICE

Physics Problems: Heat engines, Grade 8

Gas operation, engine design and efficiency.

18 problems across 3 sub-topics
Practise in the interactive mode

Here the conditions and analysis of the solution can be read without an account. In the simulator, you need to collect the same analyzes yourself: “Given,” formulas, order of steps and answer.

Problem statements

The answer options are there to check against, and the walkthrough opens under each problem.

18 problems
Position in this set: 1 from 18

Problem #22

Work done by gas and how engines work

What concept does the description correspond to: “Gas performs mechanical work when it expands and moves the piston or turbine blades.»?

Answer options

  1. \text{Work done by an expanding gas}
  2. \text{Internal combustion engine}
  3. \text{Steam turbine}
  4. \text{Capillary action}
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Given
\text{Description}
\text{Gas performs mechanical work when it expands and moves the piston or turbine blades.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    Some of the internal energy of the gas is converted into mechanical energy, and compression by an external force can increase the internal energy.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Work done by an expanding gas}

Answer\text{Concept} = \text{Work done by an expanding gas}

Position in this set: 2 from 18

Problem #23

Work done by gas and how engines work

What concept does the description correspond to: “A heat engine in which fuel is burned inside a cylinder and the expanding gas acts on a piston.»?

Answer options

  1. \text{Internal combustion engine}
  2. \text{Work done by an expanding gas}
  3. \text{Steam turbine}
  4. \text{Capillary action}
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Given
\text{Description}
\text{A heat engine in which fuel is burned inside a cylinder and the expanding gas acts on a piston.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    The four-stroke cycle comprises intake, compression, power and exhaust. Useful work is produced mainly during the power stroke.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Internal combustion engine}

Answer\text{Concept} = \text{Internal combustion engine}

Position in this set: 3 from 18

Problem #24

Heat engines

During which stroke of a four-stroke engine do heated gases directly perform useful work on the piston?

Answer options

  1. \text{worker move}
  2. \text{Intake}
  3. \text{Compression}
  4. \text{Issue}
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Given
\text{cycle}
\text{four tact}
Find

\text{beat useful work}

  1. \text{After ignition Gas pressure sharply growing}
  2. \text{gas expanding and pushes piston}\text{worker move}

Answer\text{worker move}

Position in this set: 4 from 18

Problem #25

Heat engine efficiency and the environment

What concept does the description correspond to: “A device that operates in cycles, receiving heat from a hot reservoir, doing work and rejecting some energy to a cold reservoir.»?

Answer options

  1. \text{Heat engine}
  2. \text{Heat engine efficiency}
  3. \text{Impact of heat engines}
  4. \text{Capillary action}
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Given
\text{Description}
\text{A device that operates in cycles, receiving heat from a hot reservoir, doing work and rejecting some energy to a cold reservoir.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    It is impossible to convert all the heat received into work, so the efficiency of any real heat engine is less than one.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Heat engine}

Answer\text{Concept} = \text{Heat engine}

Position in this set: 5 from 18

Problem #26

Heat engine efficiency and the environment

What concept does the description correspond to: “The ratio of net work produced by a heat engine per cycle to heat supplied to its working substance by the hot reservoir during the same cycle.»?

Answer options

  1. \text{Heat engine efficiency}
  2. \text{Heat engine}
  3. \text{Impact of heat engines}
  4. \text{Capillary action}
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Given
\text{Description}
\text{The ratio of net work produced by a heat engine per cycle to heat supplied to its working substance by the hot reservoir during the same cycle.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    For the engine, η = A/Q₁. Heat Q₁ reaching the working substance may be less than the energy qm released by fuel. For the whole installation evaluated against fuel input, use A/(qm), including heat-transfer losses. Do not mix these calculation boundaries.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Heat engine efficiency}

Answer\text{Concept} = \text{Heat engine efficiency}

Position in this set: 6 from 18

Problem #27

Heat engines

The engine received 400 kJ from the fuel and performed 120 kJ of useful work. Find the efficiency.

Answer options

  1. 30\,\%
  2. 12\,\%
  3. 70\,\%
  4. 333\,\%
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Given
A
120\,\text{кДж}
Q_1
400\,\text{кДж}
Find

\eta

  1. \eta=\frac{A}{Q_1}\eta=\frac{120}{400}\eta = 0{,}3
  2. \eta=30\,\%

Answer30\,\%

Position in this set: 7 from 18

Problem #115

Work done by gas and how engines work

Gas expands at constant pressure 100000 Pa, increasing the volume by 0{,}002 m³. Find the work done by the gas.

Answer options

  1. 200\,\text{Дж}
  2. 400\,\text{Дж}
  3. 100\,\text{Дж}
  4. 600\,\text{Дж}
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Given
p
100000\,\text{Па}
V
0{,}002\,\text{м}^{3}
Find

A

  1. A=p\Delta VA=100000 \cdot 0{,}002A=200\,\text{Дж}

    During expansion, the work done by the gas is positive.

Answer200\,\text{Дж}

Position in this set: 8 from 18

Problem #116

Work done by gas and how engines work

Gas expands at constant pressure 200000 Pa, increasing the volume by 0{,}003 m³. Find the work done by the gas.

Answer options

  1. 1200\,\text{Дж}
  2. 600\,\text{Дж}
  3. 300\,\text{Дж}
  4. 1800\,\text{Дж}
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Given
p
200000\,\text{Па}
V
0{,}003\,\text{м}^{3}
Find

A

  1. A=p\Delta VA=200000 \cdot 0{,}003A=600\,\text{Дж}

    During expansion, the work done by the gas is positive.

Answer600\,\text{Дж}

Position in this set: 9 from 18

Problem #117

Work done by gas and how engines work

Gas received 1000 J of heat and expanded from 0{,}002 up to 0{,}005 m³ at constant pressure 100000 Pa. Find the change in internal energy.

Answer options

  1. 1400\,\text{Дж}
  2. 700\,\text{Дж}
  3. 350\,\text{Дж}
  4. 2100\,\text{Дж}
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Given
Q
1000\,\text{Дж}
V_1
0{,}002\,\text{м}^{3}
V_2
0{,}005\,\text{м}^{3}
p
100000\,\text{Па}
Find

\Delta U

  1. A=p(V_2-V_1)A=100000 \cdot (0{,}005 - 0{,}002)A=300\,\text{Дж}

    We find the work done by the gas itself.

  2. \Delta U=Q-A\Delta U=1000 - 300\Delta U=700\,\text{Дж}

    The remaining energy increases internal energy.

Answer700\,\text{Дж}

Position in this set: 10 from 18

Problem #118

Work done by gas and how engines work

Gas received 1800 J of heat and expanded from 0{,}003 up to 0{,}007 m³ at constant pressure 200000 Pa. Find the change in internal energy.

Answer options

  1. 2000\,\text{Дж}
  2. 500\,\text{Дж}
  3. 1000\,\text{Дж}
  4. 3000\,\text{Дж}
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Given
Q
1800\,\text{Дж}
V_1
0{,}003\,\text{м}^{3}
V_2
0{,}007\,\text{м}^{3}
p
200000\,\text{Па}
Find

\Delta U

  1. A=p(V_2-V_1)A=200000 \cdot (0{,}007 - 0{,}003)A=800\,\text{Дж}

    We find the work done by the gas itself.

  2. \Delta U=Q-A\Delta U=1800 - 800\Delta U=1000\,\text{Дж}

    The remaining energy increases internal energy.

Answer1000\,\text{Дж}

Position in this set: 11 from 18

Problem #119

Work done by gas and how engines work

Got gas first 500 J at constant volume. Then I got more 900 J and expanded by 0{,}002 m³ at pressure 100000 Pa. Find the total change in internal energy.

Answer options

  1. 2400\,\text{Дж}
  2. 600\,\text{Дж}
  3. 1200\,\text{Дж}
  4. 3600\,\text{Дж}
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Given
Q_1
500\,\text{Дж}
Q_2
900\,\text{Дж}
V
0{,}002\,\text{м}^{3}
p
100000\,\text{Па}
Find

\Delta U

  1. A=p\Delta VA=100000 \cdot 0{,}002A=200\,\text{Дж}

    With a constant amount of work there is no; it arises only at the second stage.

  2. Q=Q_1+Q_2Q=500 + 900Q=1400\,\text{Дж}

    Add up the resulting heat.

  3. \Delta U=Q-A\Delta U=1400 - 200\Delta U=1200\,\text{Дж}

    We apply the first law to the entire process.

Answer1200\,\text{Дж}

Position in this set: 12 from 18

Problem #120

Work done by gas and how engines work

Got gas first 800 J at constant volume. Then I got more 1200 J and expanded by 0{,}003 m³ at pressure 200000 Pa. Find the total change in internal energy.

Answer options

  1. 2800\,\text{Дж}
  2. 700\,\text{Дж}
  3. 4200\,\text{Дж}
  4. 1400\,\text{Дж}
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Given
Q_1
800\,\text{Дж}
Q_2
1200\,\text{Дж}
V
0{,}003\,\text{м}^{3}
p
200000\,\text{Па}
Find

\Delta U

  1. A=p\Delta VA=200000 \cdot 0{,}003A=600\,\text{Дж}

    With a constant amount of work there is no; it arises only at the second stage.

  2. Q=Q_1+Q_2Q=800 + 1200Q=2000\,\text{Дж}

    Add up the resulting heat.

  3. \Delta U=Q-A\Delta U=2000 - 600\Delta U=1400\,\text{Дж}

    We apply the first law to the entire process.

Answer1400\,\text{Дж}

Position in this set: 13 from 18

Problem #121

Heat engine efficiency and the environment

Useful installation work 300 J at energy expended 500 J. Find the efficiency as a percentage.

Answer options

  1. 120\,\text{\%}
  2. 60\,\text{\%}
  3. 30\,\text{\%}
  4. 180\,\text{\%}
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Given
A
300\,\text{Дж}
Q
500\,\text{Дж}
Find

\eta

  1. \eta=\frac{A}{Q}\cdot100\eta=\frac{300}{500} \cdot 100\eta=60\,\text{\%}

    Useful energy does not exceed expended energy.

Answer60\,\text{\%}

Position in this set: 14 from 18

Problem #122

Heat engine efficiency and the environment

Useful installation work 450 J at energy expended 1000 J. Find the efficiency as a percentage.

Answer options

  1. 90\,\text{\%}
  2. 22{,}5\,\text{\%}
  3. 45\,\text{\%}
  4. 135\,\text{\%}
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Given
A
450\,\text{Дж}
Q
1000\,\text{Дж}
Find

\eta

  1. \eta=\frac{A}{Q}\cdot100\eta=\frac{450}{1000} \cdot 100\eta=45\,\text{\%}

    Useful energy does not exceed expended energy.

Answer45\,\text{\%}

Position in this set: 15 from 18

Problem #123

Heat engine efficiency and the environment

Installation received 2000 J of energy and has efficiency 60 %. How much energy was wasted?

Answer options

  1. 1600\,\text{Дж}
  2. 400\,\text{Дж}
  3. 800\,\text{Дж}
  4. 2400\,\text{Дж}
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Given
Q
2000\,\text{Дж}
e
60\,\text{\%}
Find

R

  1. A=Q\frac{\eta}{100}A=\frac{2000 \cdot 60}{100}A=1200\,\text{Дж}

    We convert the percentage of efficiency into a share.

  2. R=Q-AR=2000 - 1200R=800\,\text{Дж}

    The losses account for the remaining energy.

Answer800\,\text{Дж}

Position in this set: 16 from 18

Problem #124

Heat engine efficiency and the environment

Installation received 3000 J of energy and has efficiency 70 %. How much energy was wasted?

Answer options

  1. 1800\,\text{Дж}
  2. 450\,\text{Дж}
  3. 2700\,\text{Дж}
  4. 900\,\text{Дж}
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Given
Q
3000\,\text{Дж}
e
70\,\text{\%}
Find

R

  1. A=Q\frac{\eta}{100}A=\frac{3000 \cdot 70}{100}A=2100\,\text{Дж}

    We convert the percentage of efficiency into a share.

  2. R=Q-AR=3000 - 2100R=900\,\text{Дж}

    The losses account for the remaining energy.

Answer900\,\text{Дж}

Position in this set: 17 from 18

Problem #125

Heat engine efficiency and the environment

Installation receives 10000 J. The first stage passes on 80 % of energy, the second turns into useful work 50 % of energy received by it. Find the total energy loss.

Answer options

  1. 12000\,\text{Дж}
  2. 3000\,\text{Дж}
  3. 18000\,\text{Дж}
  4. 6000\,\text{Дж}
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Given
Q
10000\,\text{Дж}
e_1
80\,\text{\%}
e_2
50\,\text{\%}
Find

R

  1. E=Q\frac{\eta_1}{100}E=\frac{10000 \cdot 80}{100}E=8000\,\text{Дж}

    In the second stage, only the energy after the first is available.

  2. A=E\frac{\eta_2}{100}A=\frac{8000 \cdot 50}{100}A=4000\,\text{Дж}

    The efficiencies of the stages are multiplied, not added.

  3. R=Q-AR=10000 - 4000R=6000\,\text{Дж}

    Subtract the final useful work from the initial energy.

Answer6000\,\text{Дж}

Position in this set: 18 from 18

Problem #126

Heat engine efficiency and the environment

Installation receives 20000 J. The first stage passes on 75 % of energy, the second turns into useful work 60 % of energy received by it. Find the total energy loss.

Answer options

  1. 11000\,\text{Дж}
  2. 22000\,\text{Дж}
  3. 5500\,\text{Дж}
  4. 33000\,\text{Дж}
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Given
Q
20000\,\text{Дж}
e_1
75\,\text{\%}
e_2
60\,\text{\%}
Find

R

  1. E=Q\frac{\eta_1}{100}E=\frac{20000 \cdot 75}{100}E=15000\,\text{Дж}

    In the second stage, only the energy after the first is available.

  2. A=E\frac{\eta_2}{100}A=\frac{15000 \cdot 60}{100}A=9000\,\text{Дж}

    The efficiencies of the stages are multiplied, not added.

  3. R=Q-AR=20000 - 9000R=11000\,\text{Дж}

    Subtract the final useful work from the initial energy.

Answer11000\,\text{Дж}

The theory behind these problems

Work through the topic if a problem will not give in.

Work done by gas and how engines workGas expansion, the internal combustion engine and the steam turbine.Heat engine efficiency and the environmentEnergy conversion, inevitable losses and environmental consequences.

Formulas by topic

Look up symbols and units of measurement in the reference.

Efficiencyη · %WorkA · Дж