An ideal monatomic gas contracts in an isobaric process from 1.25 m^9 to 0.500 m^3 at a constant

An ideal monatomic gas contracts in an isobaric process from...

Key Concepts

Monatomic Gas

A monatomic gas consists of individual atoms rather than molecules. For such gases, the degrees of freedom are limited, which directly influences their internal energy expressions and heat capacities. This simplification is important in thermodynamics as it allows for the use of specific formulas, such as U = (3/2)nRT, to calculate changes in internal energy.

First Law of Thermodynamics

The first law of thermodynamics is the principle of energy conservation applied to thermodynamic systems. It states that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system. This law serves as the foundation for analyzing energy transfer processes in any thermodynamic system.

Ideal Gas Law

The ideal gas law (PV = nRT) provides a relationship between pressure, volume, number of moles, and temperature for an ideal gas. This fundamental equation is used to relate state variables in thermodynamic processes and is instrumental in determining conditions such as temperature changes when volume and pressure undergo controlled alterations.

Heat Transfer

Heat transfer in thermodynamics refers to the energy exchanged between a system and its surroundings due to a temperature difference. In a process, the amount of heat added or removed from the system combines with the work done to produce a net change in the system's internal energy, as described by the first law of thermodynamics.

Ideal Gas

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions and do not exhibit intermolecular forces. This concept allows for the derivation of simple mathematical relationships between pressure, volume, and temperature, which are foundational in the study of thermodynamics.

Work Done in Thermodynamic Processes

Work done in a thermodynamic process, especially during an isobaric process, is defined as the product of the pressure and the change in volume (W = P?V). The sign of the work indicates whether energy is being expended by the system or compressed into it, which is essential when calculating the net energy changes in a cycle or process.

Isobaric Process

An isobaric process is a thermodynamic process that occurs at constant pressure. In these processes, changes in volume directly affect the work done by or on the system, and the relationship between heat transfer and temperature change can be determined using thermodynamic principles. This concept is crucial when considering how energy is transferred in systems at constant pressure.

Internal Energy Change

The change in internal energy of a system is indicative of how the microscopic energy, such as kinetic energy of molecules, shifts during a process. For an ideal gas, and particularly a monatomic gas, this change is typically proportional to the change in temperature, and is computed using specific heat capacity at constant volume. This concept links the microscopic behavior of particles with macroscopic thermodynamic quantities.

Transcript

00:03 So for part a, the work done is going to be equalling the negative pressure times the change in volume.

00:07 This is going to be equaling to negative 1 .50 times 10 to the 5th pascal's multiplied by 0 .50 cubic meters minus 1 .25 cubic meters.

00:23 And so the work done is going to be equaling to 1 .13 times 10 to the 5th joules.

00:30 This would be our final answer for part a.

00:34 For part b, we know that the change in the internal energy would be equaling the number of moles times the molar heat capacity at a constant volume times the change in temperature.

00:44 We have a monotomic gas.

00:50 So we can say that our molar heat capacity at a constant volume would be equaling the number of degrees of freedom for a monotomic grass, three degrees of freedom multiplied by the idle gas constant are divided by two.

01:02 And so we know that for the ideal gas law applied to a constant pressure process, the number of moles times the change in temperature would be equalling the pressure times the change in volume divided by r, the ideal gas constant.

01:17 And so our change in our internal energy would be equalling the molar heat capacity 3r over 2 multiplied by the pressure times the change in volume divided by r.

01:30 And this is giving us three halves times the pressure times the change in volume.

01:35 And so our change in our internal energy would be three halves times 1 .50 times 10 to the 5th pascal's multiplied by 0 .500 minus 1 .25 units cubic meters...

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