The Structure of a Thermodynamic Application

In our case, the task is to calculate the amount of work required to compress a gas at pressure and temperature f to a pressure P2. We turn to the first law in the version of Equation 2.7, which allows us to translate the original, technical, question into one of thermodynamics  

We assume that the compression is adiabatic it will take place without exchange of heat with the environment, Qout = 0. So the first law tells us that Win is known if we know the change in enthalpy of the gas. For this we need to know how the gas enthalpy is a function of pressure and temperature. 

Assuming, for simplicity, that the gas behaves like an ideal gas, for which the enthalpy is not a function of pressure, we end up with the relation 

we assume that the process takes place reversibly, and thus 

With the assumptions that the gas behaves as an ideal gas and c is not a function of temperature, we may write 

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