Two moles of ideal gas with molar specific heat cV=(5)/(2) R are at T=300 K and P=100 kPa. Dete

step 1 Hello and welcome to this video solution of numerate. This question is based on the principles o

Two moles of ideal gas with molar specific heat cV=(5)/(2) R...

Key Concepts

Thermodynamic Work

Work in thermodynamics is the energy transfer associated with a force causing displacement, such as during the expansion or compression of a gas. The amount of work done depends on the process path, which is why different processes (isothermal, constant volume, constant pressure) yield different work values even with the same heat input.

Specific Heat Capacities

Specific heat capacities, such as cV for processes at constant volume, quantify the amount of heat required to raise the temperature of a mole of a substance by one degree. Understanding these values is crucial for relating the heat input to temperature changes in specific thermodynamic pathways.

Constant Pressure Process

A constant pressure process maintains a fixed pressure while allowing the volume to change. Heat added in this process not only alters the internal energy (changing the temperature) but also does work as the gas expands or contracts.

Constant Volume Process

In a constant volume process, the volume of the gas remains unchanged, meaning that no work is done by the gas. Thus, any heat added changes the internal energy directly, resulting in a change in temperature.

Isothermal Process

An isothermal process occurs at a constant temperature. In such processes, any heat added to the system is entirely used to perform work, as the internal energy of an ideal gas depends solely on temperature.

First Law of Thermodynamics

The first law is a statement of energy conservation, asserting that the change in a system’s internal energy equals the heat added to the system minus the work done by the system. This principle is essential in determining how heat input translates into temperature changes and work output.

Ideal Gas Law

This fundamental relation in thermodynamics connects the pressure, volume, temperature, and number of moles of an ideal gas. It provides the basis for understanding how changes in one variable affect the others, which is vital when analyzing different thermodynamic processes.

Transcript

00:01 Hello and welcome to this video solution of numerate.

00:04 This question is based on the principles of thermodynamics.

00:07 Here we are given with two moles of ideal gas.

00:11 So let me quickly write down the variables.

00:14 So n equal to 2 moles and equal to 2 moles of ideal gas are there and the specific heat cv is equal to i tried specific heat cv specific heat at constant volume which is equal to 5 by 2 r the temperature t is 300 kelvin it's given this is the initial temperature t equal to 300 kelvin pressure is 100 kilobaskar now we have to determine the final temperature and the work done of the gas when 1 .5 kilojoule of heat is added so amount of heat added is q which is 1 .5 kilojoule 5 kilo and we can write it as 1 500 jule first of all so part a so the heat is added at isothermal condition isothermal for isothermal we know that the temperature remains constant so it is implied that the temperature will be equal to 300 kelvin so we have the temperature after this isothermal process now we need to calculate the work done by the gas also we know that okay so first of all let us write the equation first law of thermodynamics that is q the heat transfer by to a gas is equal to the change in internal energy that is del u plus the external work done w now for isothermal process for no change in temperature we have del q equal to 0 so this will be equal to 0 so we have got work done is equal to q thus we can say the work done by the gas is equal to 1 .5 kilojoule so we have got both this temperature as 300 kelvin and work done as 1 .5 kilojou for this isothermal condition now we move on to part b which tells us that the heat is added at constant volume so del v is equal to constant, right? or 0, del v equal to 0.

03:31 The volume is constant means the change in volume is actually 0.

03:35 So here we have for del v equal to 0, the work done by the gas, which is given as p del v, this is equal to 0...

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