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7. (II) In an engine, an almost ideal gas is compressed adia- batically to half its volume. In doing so, 2630 J of work is done on the gas. (a) How much heat flows into or out of the gas? (b) What is the change in internal energy of the gas? (c) Does its temperature rise or fall?

7. (II) In an engine, an almost ideal gas is compressed adia- batically to half its volume. In doing so, 2630 J of work is done on the gas. (a) How much heat flows into or out of the gas? (b) What is the change in internal energy of the gas? (c) Does its temperature rise or fall?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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**Problem 7: Adiabatic Compression of an Ideal Gas** In an engine, an almost ideal gas is compressed adiabatically to half its volume. In doing so, 2630 J of work is done on the gas. (a) How much heat flows into or out of the gas? (b) What is the change in internal energy of the gas? (c) Does its temperature rise or fall? --- Explanation: This problem involves the adiabatic compression of an ideal gas. Adiabatic processes are thermodynamic processes in which no heat is exchanged between the system and the surroundings. Thus, the internal energy change in the gas is equal to the work done on it, since no heat enters or leaves the system. To provide the specific answers: (a) **Heat Flow (Q):** In an adiabatic process, no heat flows into or out of the gas, therefore: \[ Q = 0 \] (b) **Change in Internal Energy (ΔU):** The change in internal energy of the gas, ΔU, is given by the first law of thermodynamics, which in the case of an adiabatic process simplifies to: \[ \Delta U = W \] Given that 2630 J of work is done on the gas, the change in internal energy is: \[ \Delta U = 2630 \, \text{J} \] (c) **Temperature Change:** Since the internal energy of an ideal gas is directly related to its temperature, and work is done on the gas, its internal energy increases. As a result, the temperature of the gas rises when it is compressed adiabatically. Hence, the temperature rises.
Transcribed Image Text:**Problem 7: Adiabatic Compression of an Ideal Gas** In an engine, an almost ideal gas is compressed adiabatically to half its volume. In doing so, 2630 J of work is done on the gas. (a) How much heat flows into or out of the gas? (b) What is the change in internal energy of the gas? (c) Does its temperature rise or fall? --- Explanation: This problem involves the adiabatic compression of an ideal gas. Adiabatic processes are thermodynamic processes in which no heat is exchanged between the system and the surroundings. Thus, the internal energy change in the gas is equal to the work done on it, since no heat enters or leaves the system. To provide the specific answers: (a) **Heat Flow (Q):** In an adiabatic process, no heat flows into or out of the gas, therefore: \[ Q = 0 \] (b) **Change in Internal Energy (ΔU):** The change in internal energy of the gas, ΔU, is given by the first law of thermodynamics, which in the case of an adiabatic process simplifies to: \[ \Delta U = W \] Given that 2630 J of work is done on the gas, the change in internal energy is: \[ \Delta U = 2630 \, \text{J} \] (c) **Temperature Change:** Since the internal energy of an ideal gas is directly related to its temperature, and work is done on the gas, its internal energy increases. As a result, the temperature of the gas rises when it is compressed adiabatically. Hence, the temperature rises.
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