Five moles of a monatomic ideal gas expand adiabatically,...

Five moles of a monatomic ideal gas expand adiabatically, and its temperature decreases from 370 to $290 \mathrm{~K}$. Determine (a) the work done (including the algebraic sign) by the gas, and (b) the change in its intemal energy.

Key Concepts

Work Done in Thermodynamic Processes

Work in thermodynamics refers to the energy transferred when a system undergoes expansion or compression. In the context of an adiabatic process, since no heat is transferred, the work done by or on the system is equal to the negative change in internal energy. This concept helps in identifying how energy is allocated between work and internal energy changes.

Internal Energy of a Monatomic Ideal Gas

For a monatomic ideal gas, the internal energy is solely a function of its temperature and is given by U = (3/2)nRT, where n is the number of moles and R is the universal gas constant. This relationship is vital for determining how changes in temperature influence the internal energy during thermodynamic processes.

Adiabatic Process

In an adiabatic process, no heat is exchanged between the system and its environment, meaning that the heat transfer (q) is zero. Consequently, any work done by or on the system directly affects its internal energy, which is a key factor in analyzing the behavior of the gas during expansion or compression.

First Law of Thermodynamics

This principle states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings. This law provides the foundational relationship between energy transfer, work, and internal energy changes in any thermodynamic process.

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