For each of the following adiabatic processes, find the...

For each of the following adiabatic processes, find the change in internal energy. ( $a$ ) A gas does $5 \mathrm{~J}$ of work while expanding adiabatically. (b) During an adiabatic compression, $80 \mathrm{~J}$ of work is done on a gas. During an adiabatic process, no heat is transferred to or from the system. (a) $\Delta U=\Delta Q-\Delta W=0-5 \mathrm{~J}=-5 \mathrm{~J}$ (b) $\Delta U=\Delta Q-\Delta W=0-(-80 \mathrm{~J})=+80 \mathrm{~J}$

For each of the following adiabatic processes, find the change in internal energy. ( $a$ ) A gas does $5 \mathrm{~J}$ of work while expanding adiabatically. (b) During an adiabatic compression, $80 \mathrm{~J}$ of work is done on a gas.
During an adiabatic process, no heat is transferred to or from the system.
(a) $\Delta U=\Delta Q-\Delta W=0-5 \mathrm{~J}=-5 \mathrm{~J}$
(b) $\Delta U=\Delta Q-\Delta W=0-(-80 \mathrm{~J})=+80 \mathrm{~J}$

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Key Concepts

Sign Conventions in Thermodynamics

Understanding sign conventions is crucial in thermodynamics, particularly when distinguishing between work done by the system and work done on the system. Typically, work done by the system is taken to be positive and work done on the system is negative in the context of the first law, which affects the calculation of changes in internal energy.

First Law of Thermodynamics

The First Law of Thermodynamics is a statement of energy conservation that relates the change in internal energy of a system to the heat exchanged with its surroundings and the work done by or on the system. Expressed mathematically as ?U = Q - W, this principle is fundamental to analyzing energy transformations in any thermodynamic process.

Adiabatic Process

An adiabatic process is one in which no heat is transferred between the system and its surroundings, meaning Q equals zero. In such processes, any change in the system's internal energy is solely due to the work performed on or by the system, making analysis simpler since only work contributes to energy changes.

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