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11. (II) Use the conservation of energy to explain why the temperature of a well-insulated gas increases when it is compressed-say, by pushing down on a piston-whereas the temperature decreases when the gas expands. Show your reasoning.

11. (II) Use the conservation of energy to explain why the temperature of a well-insulated gas increases when it is compressed-say, by pushing down on a piston-whereas the temperature decreases when the gas expands. Show your reasoning.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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**Question 11:** **(II)** Use the conservation of energy to explain why the temperature of a well-insulated gas increases when it is compressed—say, by pushing down on a piston—whereas the temperature decreases when the gas expands. Show your reasoning. **Explanation:** To understand this phenomenon, we need to delve into the principles of the conservation of energy and thermodynamics. When a gas is compressed in a well-insulated container (an adiabatic process), no heat is exchanged with the surroundings. The work done on the gas increases its internal energy, which manifests as an increase in the temperature of the gas. Conversely, when the gas expands, it does work on its surroundings. Since the process is adiabatic, the gas cannot gain heat from outside sources. Therefore, its internal energy decreases, leading to a drop in temperature. Here is a detailed breakdown of the reasoning: **Compression:** - **Work Done on Gas:** When you compress the gas by pushing down on a piston, you are doing work on the gas. - **Energy Conservation:** In a well-insulated system, the energy for the work comes from the internal energy of the gas. - **Increased Internal Energy:** Because the gas can't lose energy to the outside (no heat loss), the work done on the gas increases its internal energy. - **Temperature Increase:** An increase in internal energy results in an increase in the temperature of the gas. **Expansion:** - **Work Done by Gas:** When the gas expands, it does work on the piston or on the surroundings. - **Energy Conservation:** Since the system is insulated, it cannot absorb heat from the surroundings. - **Decreased Internal Energy:** The work done by the gas comes from its internal energy, leading to a decrease in that energy. - **Temperature Decrease:** A decrease in internal energy results in a decrease in the temperature of the gas. This explanation highlights the relationship between work, internal energy, and temperature changes in an adiabatic process, where the conservation of energy principle plays a crucial role.
Transcribed Image Text:**Question 11:** **(II)** Use the conservation of energy to explain why the temperature of a well-insulated gas increases when it is compressed—say, by pushing down on a piston—whereas the temperature decreases when the gas expands. Show your reasoning. **Explanation:** To understand this phenomenon, we need to delve into the principles of the conservation of energy and thermodynamics. When a gas is compressed in a well-insulated container (an adiabatic process), no heat is exchanged with the surroundings. The work done on the gas increases its internal energy, which manifests as an increase in the temperature of the gas. Conversely, when the gas expands, it does work on its surroundings. Since the process is adiabatic, the gas cannot gain heat from outside sources. Therefore, its internal energy decreases, leading to a drop in temperature. Here is a detailed breakdown of the reasoning: **Compression:** - **Work Done on Gas:** When you compress the gas by pushing down on a piston, you are doing work on the gas. - **Energy Conservation:** In a well-insulated system, the energy for the work comes from the internal energy of the gas. - **Increased Internal Energy:** Because the gas can't lose energy to the outside (no heat loss), the work done on the gas increases its internal energy. - **Temperature Increase:** An increase in internal energy results in an increase in the temperature of the gas. **Expansion:** - **Work Done by Gas:** When the gas expands, it does work on the piston or on the surroundings. - **Energy Conservation:** Since the system is insulated, it cannot absorb heat from the surroundings. - **Decreased Internal Energy:** The work done by the gas comes from its internal energy, leading to a decrease in that energy. - **Temperature Decrease:** A decrease in internal energy results in a decrease in the temperature of the gas. This explanation highlights the relationship between work, internal energy, and temperature changes in an adiabatic process, where the conservation of energy principle plays a crucial role.
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