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Physics Chapter 8 : Topic 16
Carnot Engine
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Carnot’s engine is an ideal heat engine that operates:
Reasoning: A Carnot engine works between a high-temperature source and a low-temperature sink.
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The main purpose of Carnot’s engine is to:
Reasoning: Carnot’s engine represents the most efficient possible heat engine.
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The working principle of Carnot’s engine is based on:
Reasoning: Carnot’s cycle consists of two isothermal and two adiabatic reversible processes.
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The working substance of a Carnot engine is usually:
Reasoning: An ideal gas is used as the working substance because it can undergo reversible expansion and compression.
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A Carnot engine operates between:
Reasoning: The engine absorbs heat from a hot reservoir and rejects some heat to a cold reservoir.
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The first process in the Carnot cycle is:
Reasoning: The gas first expands isothermally while absorbing heat from the hot reservoir.
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During isothermal expansion of Carnot’s engine:
Reasoning: In isothermal expansion, the gas absorbs heat from the source while maintaining constant temperature.
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During adiabatic expansion in Carnot’s cycle:
Reasoning: Adiabatic processes occur without heat transfer.
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In the isothermal compression process of Carnot’s cycle:
Reasoning: During isothermal compression, the gas releases heat to the cold reservoir.
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During adiabatic compression in Carnot’s engine:
Reasoning: Work done on the gas increases its temperature without heat exchange.
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A Carnot cycle contains:
Reasoning: These four reversible processes complete the Carnot cycle.
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The expansion process in Carnot engine produces:
Reasoning: Expansion of the gas pushes the piston and performs work.
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The efficiency of a Carnot engine depends on:
Reasoning: Carnot efficiency depends only on the temperatures of the two reservoirs.
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The efficiency of a Carnot engine is given by:
Reasoning: Carnot efficiency depends on absolute temperatures of hot and cold reservoirs.
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If the temperature of the hot reservoir increases, Carnot efficiency:
Reasoning: A higher source temperature increases the temperature difference.
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If the temperature of the cold reservoir decreases, Carnot efficiency:
Reasoning: Lower sink temperature increases the fraction of heat converted into work.
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A Carnot engine operating between $\mathbf{600\ K}$ and $\mathbf{300\ K}$ has efficiency:
Reasoning: $\mathbf{\eta = 1 -}$ $\frac{\mathbf{T}_{\mathbf{C}}}{\mathbf{T}_{\mathbf{H}}}\mathbf{= 1 -}\frac{\mathbf{300}}{\mathbf{600}}\mathbf{= 0.5 = 50\%}$
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A Carnot engine cannot have $\mathbf{100\%}$ efficiency because:
Reasoning: The second law requires heat rejection to a lower-temperature reservoir.
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The maximum efficiency of any heat engine is:
Reasoning: Carnot efficiency is the theoretical maximum efficiency.
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Two heat engines operate between the same temperatures. The more efficient engine is:
Reasoning: No real engine can exceed the efficiency of a reversible Carnot engine.
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Carnot engine is considered ideal because:
Reasoning: Carnot engine assumes reversible processes without friction or energy losses.
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A reversible Carnot engine produces:
Reasoning: Reversible operation gives the highest possible efficiency.
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The area enclosed by the Carnot cycle on a $\mathbf{P - V}$ diagram represents:
Reasoning: The area inside a cyclic $\mathbf{P - V}$ graph represents work done by the engine.
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The net change in internal energy of the working substance after one Carnot cycle is:
Reasoning: The system returns to its original state after completing the cycle.
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During one complete Carnot cycle:
Reasoning: According to the first law, the net heat supplied becomes net work output.
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A Carnot engine absorbs $\mathbf{800\ J}$ heat and rejects $\mathbf{500\ J}$ heat. The work output is:
Reasoning: $\mathbf{W =}\mathbf{Q}_{\mathbf{H}}\mathbf{-}\mathbf{Q}_{\mathbf{C}}\mathbf{= 800 - 500 = 300\ J}$
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If a Carnot engine has efficiency 40%, the ratio of rejected heat to absorbed heat is:
Reasoning: $\mathbf{\eta = 1 -}$ $\frac{\mathbf{Q}_{\mathbf{C}}}{\mathbf{Q}_{\mathbf{H}}}$ $\mathbf{\Longrightarrow}$ $\mathbf{0.4 = 1 -}$ $\frac{\mathbf{Q}_{\mathbf{C}}}{\mathbf{Q}_{\mathbf{H}}}$ $\mathbf{\Longrightarrow}$ $\frac{\mathbf{Q}_{\mathbf{C}}}{\mathbf{Q}_{\mathbf{H}}}\mathbf{= 0.6}$
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A Carnot engine has zero efficiency when:
Reasoning: $\mathbf{\eta = 1 -}$ $\frac{\mathbf{T}_{\mathbf{C}}}{\mathbf{T}_{\mathbf{H}}}$When $\mathbf{T}_{\mathbf{C}}\mathbf{=}\mathbf{T}_{\mathbf{H}}$, efficiency becomes zero.
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Which factor does NOT affect Carnot efficiency?
Reasoning: Carnot efficiency depends only on reservoir temperatures.
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The working principle of Carnot’s engine proves that:
Reasoning: Carnot engine establishes the theoretical upper limit of heat engine efficiency.
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