A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P 22.67 .

step 1 Hi friends for one mole of mono atomic gas pavie graph is given. A to be process is is isotherma

A 1.00-mol sample of an ideal monatomic gas is taken through...

Key Concepts

Ideal Gas Law

This fundamental relation, expressed as PV = nRT, connects pressure, volume, and temperature in an ideal gas. It serves as the basis for calculating state variables during any process involving an ideal gas and is essential for understanding how the gas behaves under different conditions.

Isothermal Process

An isothermal process is one in which the temperature remains constant throughout. For an ideal gas undergoing this kind of process, the internal energy does not change, meaning that any energy transferred as heat into the system is entirely used to do work, and vice versa.

Reversible Process

A reversible process is an idealized transformation that occurs infinitely slowly so that the system remains in thermodynamic equilibrium. This concept is crucial because it represents the maximum possible work output and efficiency that can be achieved under given conditions.

Thermodynamic Cycle

A thermodynamic cycle consists of a series of processes that return a system to its initial state. In these cycles, work and heat are exchanged between the system and its surroundings, and the net work done is determined by the area enclosed by the cycle on a pressure-volume diagram.

Work in Thermodynamic Processes

In the context of gas processes, work is often determined by integrating the pressure with respect to the change in volume. For reversible processes, this calculation gives the total work done by or on the gas, playing a key role in energy balance analyses.

First Law of Thermodynamics

This law is the conservation of energy applied to thermodynamic systems, stating 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. It is central to analyzing energy transfers in any thermodynamic process.

Efficiency

Efficiency in thermodynamics is defined as the ratio of the work output to the heat input. It measures how effectively a cyclic process converts heat into work and is a critical parameter in evaluating the performance of engines and other thermodynamic devices.

Carnot Efficiency

Carnot efficiency represents the maximum efficiency attainable by any heat engine operating between two thermal reservoirs. It depends solely on the temperatures of these reservoirs and sets an upper limit that no real engine can exceed, making it a benchmark for comparing the performance of other thermodynamic cycles.

Transcript

00:02 Hi friends for one mole of mono atomic gas pavie graph is given.

00:25 A to be process is is isothermal expansion.

00:36 We have to calculate in the part a net work done and b part amount of the heat absorb amount of the heat rejected efficiency compare efficiency with with efficiency of car not working for same temperature difference let us see here first part in the first part we have to calculate work done so work done for the process a to v minus p avava lawn of volume at b upon volume at a 5 into 1 .013 10 to the power 5 volume in meter cube 10 into 10 to the power minus 3 lon of 50 upon 10 so it is to be minus 8150 jule b2c is is obaric process so work done in b2c pressure at b into change in volume pressure at b is given one atmosphere volume at a is 10 liter volume at b becomes 50 liter so it is to be 4 .50 jules process c2a is is is is is is is so work done is zero so work done in c2a is zero because c2a change in volume is zero hence network done we will get work done in the process a to b, work done in the process v to c and worked done in the process c2a minus 8150 plus 4050 plus 0 that is 4100 jule now b part amount of energy added to the guess that will be in the process a to b p a b b b b b b a loan of volume at b upon volume at a 5 into 1 .013 10 to the power of 5 10 into 10 to the power minus 3 loan of 50 upon 10 so it is to be 8 1 5 jr.

04:29 Now in c per we have to find heat added to the gas in the process c2a it is to be vcv into delta t that is 3 by 2 r temperature at a minus temperature at c that is 3 by 2 r p a v a upon r minus pc vc upon r so it can be written as 352 into 8 .314 pressure at a is 5 atmosphere into volume is 10 liter pressure at c becomes one atmosphere volume is one 10 liter sorry 8 .314 8 .314 so it is to be 6080 jule energy added to the gas by heat you added q a v plus qca 818 818 8 1 560 6080 so it is 1420 july energy exhausted from the system or rejected heat 5 by 2 pv bc minus bv substitute to the value 1 .013 10 to the power 5 10 into 10 to the power minus 3 minus 50 into 10 to the power minus 3 so it is to be minus 101 jude or 10 .1 kilojoude...

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