Home page for accesible maths 2 Chapter 2 contents 2.8 Partial differentiation in more than two variables 2.10 Solution

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2.9 Physical applications of partial differentiation

Remark. In applications, quantities can depend upon many different variables. For example, the speed of an airliner will be influenced by the air pressure, temperature, humidity, wind speed etcetera.

Example.

The equation of state of an ideal gas is

k=A\exp\Bigl({{TS-H}\over{RT}}\Bigr),

where $k,R$ and $A$ are constants and $H,S$ and $T$ are variables. Find ${{\partial H}\over{\partial T}}$ , the rate of change of $H$ as $T$ changes, but $S$ stays constant.