Natural convection: air. Show that \(\beta=1 / T\) for an ideal gas.
Repeat the example above for air instead of water.
Which fluid generates more circulation? Suggest a reason for this.

Example above:

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Example 13.3. A mixture of methanol and water at 90 C containing 40% by mole of methanol is in contact with a cold wall. Find the rate of condensation and the composition of the condensate formed at this point. Assume an interface temperature of 85 C. The data needed are of two types: (i) physical properties and (ii) transport properties or values for the transport coefficients. We use the following values for illustration of the calculation method. (i) Physical properties. The specific heats of components in the gas phase (methanol = 1 and water = 2) are Cp.g1 = 45 J/mol - K and Cp.g2 = 34J/mol. K. The heats of condensation are AH1,1 = 36 000 J/mol and AHg1.2 = 43 000 J/mol. The Antoine constants with pressure in pascals and temperature in K are A 23.402, B = 3593.4, C = -34.92, A2 = 23.196, B = 3816.4, and C = -46.13. (ii) Transport properties or coefficients. The gas-side heat transfer coefficient 60 W/m. K The gas-side mass transfer coefficient 0.08 m/s. The liquid-side mass transfer coefficient is not needed for this model. = The liquid-side composition at the interface is fixed by assuming that the mole fraction in the liquid for each component is proportional to its condensation rate, i.e., x1 = N/NT This is referred to as the completely unmixed assumption for the condensate. The assumption implies an infinite resistance on the liquid side.