A sample of a monatomic ideal gas occupies 5.00 L at...

A sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P21.63). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point $C .$ (e) Now consider the processes $A \rightarrow B, B \rightarrow C,$ and $C \rightarrow A .$ Describe how to carry out each process experimentally. (f) Find $Q, W,$ and $\Delta E_{\text { int }}$ for each of the processes. (g) For the whole cycle $A \rightarrow B \rightarrow C \rightarrow A,$ find $Q, W,$ and $\Delta E_{\text { int }}$

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics, which is the principle of energy conservation for thermodynamic systems, states that the change in a system’s internal energy (?E_int) is equal to the heat added to the system (Q) minus the work done by the system (W). This principle is critical when calculating the energy transfer during various thermodynamic processes, especially in cyclic processes where energy input and output over the cycle must balance.

Experimental Realization of Thermodynamic Processes

Experimental realization refers to the practical methods used to carry out the different thermodynamic processes. For instance, a constant volume process can be achieved by containing the gas in a rigid container, an isothermal process can be maintained by ensuring the system remains in thermal equilibrium with a large reservoir (allowing heat to flow as needed to maintain temperature), and an isobaric process can be implemented by allowing the gas to expand or contract against a piston that adjusts to maintain constant pressure. Understanding these allows one to connect theory with practical laboratory techniques.

Ideal Gas Law

The Ideal Gas Law, given by PV = nRT, is a fundamental relation in thermodynamics that correlates pressure (P), volume (V), number of moles (n), temperature (T), and the gas constant (R). This law is crucial for solving problems involving gases because it allows you to find one variable when the others are known, making it the starting point for analyzing any process a gas undergoes.

Thermodynamic Processes

Thermodynamic processes describe the changes a gas undergoes under different constraints. This concept covers special types of processes such as constant volume (isochoric), isothermal, and isobaric processes, each characterized by keeping one state variable constant while allowing the others to change. Understanding these processes helps in analyzing paths on a pressure-volume or temperature-volume diagram and determining work, heat transfer, and state variable changes.

Monatomic Ideal Gas Properties

Monatomic ideal gases, which consist of single atoms, have specific internal energy properties that depend solely on temperature. The internal energy of a monatomic ideal gas is derived from the translational kinetic energy of its particles, typically expressed as (3/2)nRT. This property simplifies calculations and is important when determining how temperature changes affect the energy content of the gas in different processes.

Transcript

00:01 Everyone here it is given.

00:02 Monoatomic gas undergoes process a2b isochoric, v2c, isothermal and c2a isoberic.

00:42 And a volume is 5 litre pressure is 1 atmosphere and temperature is 300 kelvin.

00:57 In the first part we have to find the temperature at b and b part temperature at c, in c part temperature at c and d part volume at c.

01:20 Discuss experimental method to achieve process a to b, b to c and c to a.

01:53 We have to calculate amount of heat transfer.

01:59 Work done and change in internal energy in each process we have to find total amount of heat energy transfer in a cycle work done in a cycle and change in internal energy of the cycle changing internal energy of the cycle so all these parameters we have to calculate first part using gas equation pb is equal to nr t number of moles can be related as pressure at a point into volume at a point divided by r into temperature at a point substituting the value pressure at a 1 .013 10 to the 4 5 volume volume is 5 liter but we are using in meter cube gas constant 8 .314 into 300 kelvin so answer of a part you will get 0 .203 now b part, temperature at b, a to v is isochoric process.

03:41 So, delta v is zero and temperature will be directly proportional to pressure.

03:49 So we can say temperature at b point will be temperature at a.

03:55 Pressure at b upon pressure at a, that is 300, 3 upon 1.

04:01 So it will be 900 kelvin.

04:06 Now, c point b2c is isothermal process so temperature is constant hence temperature at c will be also 900 kelvin d point c2a pressure is constant so volume is directly overshunded to temperature.

04:48 So volume at b will be sorry volume at c 15 liter e point.

05:52 A to b process can be obtained by fixing the position of piston b2c can be obtained by keeping the system inside over at nac and ended carbon and c2a can be obtained by piston to be kept free in atmosphere.

07:33 Now we have to discuss the f point change in internal energy.

07:38 So we will find the internal energy in each internal energy at a will be ncb temperature at a monotomics 3x2 r into 300 calvin substitute the value number of moles 0 .203 3 by 2, 8 .314...

Please give Ace some feedback