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Hello students, in this question we need to prove how the heat capacity of the perfect gas independent of both volume and the pressure.
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First of all we are going to see the definition for the heat capacity at constant pressure.
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It is the amount of heat that required to increase the temperature of the system by 1 degree celsius at constant pressure.
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Similarly, the heat capacity at constant volume can be defined as the amount of heat that required to increase the temperature of the system by 1 degree celsius at constant volume.
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Now, we are going to find out the ideal gas equation that is pv is equal to nrt.
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We are going to keep the pressure constant and going to differentiate this so that we will get d of pv will be equal to n is constant and r is constant dt.
01:04
On differentiating this we will get pdv plus vdp will be equal to nr dt.
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We know that the differentiation is carried out at constant pressure therefore this term be equal to 0 and the new equation will be pdv will be equal to nr dt.
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Let this be equation number 1.
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Now we are going to give the expression for the heat which is added to the system at constant volume qv which is given by cv del t.
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This will be equal to del u plus work.
01:46
Here the work done by the system will be equal to 0 and this will be equal to del u that is cv del t will be equal to del u...