When 1310 J of heat are added to one mole of an ideal...

When 1310 $\mathrm{J}$ of heat are added to one mole of an ideal monatomic gas, its temperature increases from 272 $\mathrm{K}$ to 276 $\mathrm{K}$ . Find the
work done by the gas during this process.

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Key Concepts

First Law of Thermodynamics

This fundamental principle states that energy cannot be created or destroyed, only transformed. It relates the heat added to a system to changes in the system’s internal energy and the work done by the system, typically expressed as Q = ?U + W.

Internal Energy of an Ideal Gas

For an ideal gas, the internal energy depends only on temperature. In the case of a monatomic ideal gas, the change in internal energy is given by ?U = (3/2)nR?T, which is crucial for determining how much of the added heat increases the gas's internal energy during heating.

Work Done by a Gas

Work in thermodynamics refers to the energy transferred by a system as it expands or compresses. It can be determined from the energy balance by subtracting the change in internal energy from the heat added (W = Q ? ?U), highlighting how energy input is partitioned into doing work and increasing internal energy.

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