+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Mechanical Properties Of Fluids

Question
CBSEENPH11019521
Wired Faculty App

Show that Cp – Cv = R.

Solution

Consider one mole of an ideal gas enclosed in a cylinder fitted with the movable frictionless piston.

Let the gas be heated at constant volume.
On supplying dQ amount of heat, let the temperature of the gas increase by dT. 

therefore space dQ space equals space straight m space cross times straight C subscript straight P space cross times space dT space space space space space space space space space space space equals space 1 cross times space straight C subscript straight P space cross times space dT space According space to space the space first space law space of space thermodynamics comma space dQ space equals space dU space plus space dW space space space space space space equals space dU space plus space straight P. dV space left square bracket space dV space equals space 0 right square bracket space space space space space space equals space dU space
therefore space space space space space space space dQ apostrophe equals 1 cross times straight C subscript straight p cross times dT 
By first law of thermodynamics, 
           dQ = dU + dW = dU + PdV 
rightwards double arrow    CpdT = Cv x dT + RdT 
At a constant pressure, 
P.dV = R.dT 

therefore space space space space space space space straight C subscript straight p equals straight C subscript straight v space plus space straight R space rightwards double arrow space space space space space space space straight C subscript straight p minus straight C subscript straight v equals straight R  
where  Cp, Cv and R are in same units. 
Hence, proved. 

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?

Do the gases have only one value of specific heat?

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation