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Mechanical Properties Of Fluids

Question
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Derive the equation of state for adiabatic process. Plot P versus V graph for the process.

Solution
According to the first law of thermodynamics,
                     dQ space equals space dU plus dW 
In an adiabatic process, no heat is allowed to exchange between the system and surrounding, therefore dQ = 0.
Thus, 
space space space space space space space dU space plus space PdV space equals space 0 space rightwards double arrow space straight C subscript straight P dT space plus space PdV space equals space 0 space rightwards double arrow space straight C subscript straight V dT space plus space PdV space equals space 0 space That space is comma space straight C subscript straight V dT space plus space RT over straight V dV space equals space 0 space left square bracket because space PV space equals space RT right square bracket space That space is comma space dT over straight T plus straight R over straight C subscript straight p dV over straight V space equals space 0 space rightwards double arrow space dT over straight T space plus space left parenthesis straight gamma space minus 1 right parenthesis space dV over straight V space equals space 0 space On space integrating comma space space space space space integral dT over straight T space plus space space left parenthesis straight gamma space minus 1 right parenthesis space integral dV over straight V space equals space constant rightwards double arrow space Ln space straight T space plus space space left parenthesis straight gamma space minus 1 right parenthesis space Ln space straight V space equals space constant rightwards double arrow space TV to the power of straight gamma space minus space 1 end exponent space equals space constant space comma space which space is space the space equation space of space state. space Since comma space PV space equals space space RT space we space have comma space straight T space equals space PV over straight R space therefore space TV to the power of straight gamma space minus space 1 end exponent space equals space PV over straight R straight V to the power of straight gamma space minus space 1 end exponent space equals space constant rightwards double arrow space PV to the power of straight gamma space equals space constant
P vs. V graph for an adiabatic process is as shown below. 
                      
                 
   

Some More Questions From Mechanical Properties of Fluids Chapter

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?

Do the gases have only one value of specific heat?

What is thermometry?

Define temperature.

When two bodies will be said to be in thermal equilibrium?

If two bodies are not in thermal equilibrium, then in which direction the heat will flow?

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