Isothermal and Adiabatic Processes

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An isothermal process is a physical change in which the temperature of the system remains constant throughout. For an ideal gas, it obeys Boyle's law: PV = constant. The process is very slow in practi…

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An adiabatic process is a change in which no heat is exchanged between the system and the surroundings. For an ideal gas, it obeys Poisson's law: PV^gamma = constant. The system must be perfectly insu…

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For an ideal gas, internal energy depends only on temperature. In an isothermal process, temperature remains constant, so internal energy also remains constant: delta U = 0.

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No heat exchange is allowed in an adiabatic process, so the system must be perfectly insulated from the surroundings. If a vessel had zero conductivity, even a slow process in it would be adiabatic.

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For an ideal gas undergoing an isothermal process, PV = constant for a given mass of gas. Here, P is pressure and V is volume.

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For an ideal gas undergoing an adiabatic process, PV^gamma = constant, where gamma = Cp/Cv. This relation is used for adiabatic changes of a given mass of gas.

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Given: Isothermal process, so PV = constant. Step 1: P1V1 = P2V2 Step 2: P2 = P1(V1/V2) Step 3: Since V2 = V1/2, P2 = P1(V1/(V1/2)) = 2P1 Answer: Final pressure becomes 2 times the initial pressure.

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Given: P1V1^gamma = P2V2^gamma Step 1: P2/P1 = (V1/V2)^gamma Step 2: V2 = V1/2, so P2/P1 = 2^1.4 Step 3: 2^1.4 = 2.64 Answer: Pressure increases by a factor of 2.64.