Using the first law of thermodynamics for an adiabatic process, establ

Question

Using the first law of thermodynamics for an adiabatic process, establish the relation PV=K, where y is the ratio of heat capacity at constant pressure to that at constant volume. Plot this equation on a p- diagram. What will be its slope?

22 Jan 2025

Answer :

Word Count : 509

In thermodynamics, the first law states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Mathematically, it is written as:

dU=δQ−δWdU = \delta Q - \delta W

For an adiabatic process, there is no heat exchange with the surroundings, meaning δQ=0\delta Q = 0. Therefore, the first law simplifies to:

dU=−δWdU = - \delta W

Since work done by the system is related to the pressure and volume, we can express it as:

δW=PdV\delta W = P dV

Now, the change in internal energy dUdU for an ideal gas can be written as:

dU=nCVdTdU = n C_V dT

where nn is the number of moles of the gas, CVC_V is the ____ ___ ___ ________ _______ ____.
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