Question

Show that Cp is greater than Cv .

Answer 1

⭕️At constant volume (Cv), the work done will be 0. so the whole of heat supplied is used in increasing the temperature.

⭕️At constant pressure (Cp), part of heat supplied is used by the system in doing work.

⭕️ more heat is needed to increase the temperature by a given amount.

✔️✔️for derivation :-

✔️✔️by using the 'First law of thermodynamics'

@ constant Pressure

dQ=dU+P.dV ➖➖➖(1)

At Constant Volume,

dQ=dU+P.dV

Since dV=0

Therefore dQ=dv ➖➖➖(2).

Cp=dU+P.dV

And Cv=dU

from above we can say that relation Cp is greater than Cv.

Answer 2

$\huge\mathbb\pink{ANSWER}$

What is Cp and Cv ?

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☑Cp is the specific heat at constant pressure .

☑Cv is the specific heat at constant volume

Now ,

What is specific heat ?

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☑Amount of heat that required to raise the temperature by 1°C .

Why Cp is always greater than Cv?

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As Cp is amount of heat that required to raise the temperature by 1°C when heat is given at constant pressure.

So pressure is fixed in Cp but some work may be done . So heat may produce.So more energy required to increase the temperature of system.

But ,

Cv is the amount of heat that required to raise the temperature by 1°C when heat is given at constant volume.

According to the equation

W = P∆V

if volume is constant then workdone is Zero . So no heat produced .Whole energy is used to increase the temperature of a system.

Result

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So we get that Cp > Cv

$\boxed{Hope\:it\:helps\:you}$