Mechanical Properties of Fluids

Question

What is the equation of state for isothermal process? Plot P versus V graph and P versus T graph for isothermal process for an ideal gas. Discuss the isothermal process using first law of thermodynamics.

Solution

An ideal gas equation is given by,
PV = nRT
In an isothermal process, temperature T is constant.
Therefore the equation of state for isothermal process reduces to,
PV = constant
The graph of P versus V and P versus T for an isothermal process is as shown below.

Now, according to first law of thermodynamics,

increment straight Q space equals space increment straight U space plus space straight P increment straight V space For space an space isothermal space process comma space space space space space increment straight U space equals space straight C subscript straight v increment straight T space equals space 0 space left square bracket Temperature space remains space constant right square bracket space therefore space increment straight Q space equals space straight P increment straight V space equals space increment straight W space In space an space isothermal space expansion comma space space space space space space space increment straight V space greater than thin space 0 space rightwards double arrow space increment straight Q space equals space straight P space increment straight V space greater than space 0 space That space is comma space in space an space isothermal space expansion comma space work space is space done space by space the space gas space and space heat space is space absorbed space by space the space gas space equal space to space work space done space by space the space gas. space In space isothermal space compression comma space increment straight V space less than space 0 space rightwards double arrow space increment straight Q space equals space straight P increment straight V space less than 0 space That space is comma space in space isothermal space compression comma space work space is space done on space the space gas space and space heat space is space released space by space gas space equal to space work space done space on space the space gas. space

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Mechanical Properties Of Fluids

What is the equation of state for isothermal process? Plot P versus V graph and P versus T graph for isothermal process for an ideal gas. Discuss the isothermal process using first law of thermodynamics.

Some More Questions From Mechanical Properties of Fluids Chapter

At what temperature specific heat of water is minimum?

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

What is the SI unit of molar specific heat?

Define heat capacity.

What are the units of heat capacity?

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

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