A 2.0 mol sample of an ideal monatomic gas undergoes the...

A $2.0 \mathrm{~mol}$ sample of an ideal monatomic gas undergoes the reversible process shown in Fig. $20-26 .$ The scale of the vertical axis is set by $T_{s}=400.0 \mathrm{~K}$ and the scale of the horizontal axis is set by $S_{s}=20.0 \mathrm{~J} / \mathrm{K} .$ (a) How much energy is absorbed as heat by the gas? (b) What is the change in the internal energy of the gas? (c) How much work is done by the gas?

A $2.0 \mathrm{~mol}$ sample of an ideal monatomic gas undergoes the reversible process shown in Fig. $20-26 .$ The scale of the vertical axis is set by $T_{s}=400.0 \mathrm{~K}$ and the scale of the horizontal axis is set by $S_{s}=20.0 \mathrm{~J} / \mathrm{K} .$ (a) How much energy is absorbed as heat by the gas?
(b) What is the change in the internal energy of the gas? (c) How much work is done by the gas?

Key Concepts

Work

In thermodynamic processes, work is the energy transferred when a force acts over a distance. For gases, it is often represented as the area under a process curve on a pressure-volume (PV) diagram, and it quantifies the energy expended in expanding or compressing the gas.

Ideal Gas

An ideal gas is a simplified model in which the particles do not interact except through elastic collisions and the gas obeys the ideal gas law (PV = nRT). For a monatomic ideal gas, the internal energy is solely a function of temperature and is given by (3/2)nRT.

Reversible Process

A reversible process is an idealized thermodynamic process that occurs infinitely slowly so that the system remains in equilibrium at every stage. This type of process maximizes work extraction or minimizes work input and is pivotal in establishing theoretical limits on efficiency.

First Law of Thermodynamics

The first law of thermodynamics expresses the conservation of energy, stating that any change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. It is mathematically expressed as ?U = Q - W, linking energy transfer via heat and work.

Internal Energy

Internal energy refers to the total energy contained within a system, encompassing the kinetic and potential energies at the molecular level. In a monatomic ideal gas, internal energy is directly related to temperature, with U = (3/2)nRT, indicating that temperature alone determines the energy content.

Heat Transfer

Heat transfer in thermodynamics is the process by which energy is exchanged between systems due to a temperature difference. In any thermodynamic process, the amount of heat transferred influences changes in internal energy and the amount of work done.

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