Propiedades termicas 1. Compute the integral of Eq. (18.31) , v2 f(v)dv and compare this result with (v2)med given by Eq. (18.16). hint: you can use tabulated integral. x2me-602 dx - 143 45 +44 (2n - 1) 2n+1a" Where n is a positive integer and a is a positive constant. 2. Calculate the integral of equation (18.30), J, of (v)dv. and compare your result with v_med given by equation (18.35). (hint: make the change of variable v= = x and use the tabulated integral n! xle -"x dx = an+1 Where n is a positive integer and a is a positive constant. 3. Explain why it is a gas of N molecules the number of molecules whose speed is in the finite interval from vav + Av es AN = N J f(v) dv .B)|if Av is small, f(v) is approximately constant on the interval, and AN & Nf (v) . For gaseous oxygen (02, molar mass= 32.0 g/mol) at T=300 K, use this approximation to calculate the number of molecules whose speed is at Av=20m/s or less than 7 v mp, D) Repeat parts b) and c) for a temperature of 600 K. e) repeat parts b) and c) for a temperature of 150 K f) what do these results tell you about the shape of the distribution as a function of the temperature? Do your conclusions agree with what you show in Figure 18.26? 4. Meteorology. Vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. Relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water at that same temperature. Expressed as a percentage. Air is saturated when the humidity is 100% (a) the vapor pressure of water at 20.0'C and the relative humidity is 60%, determine the partial pressure of water vapor in the atmosphere (that is, the pressure due exclusively steamed). B) Under the conditions of part a) what mass of water is there in 1.00 m3 of air? (The molar mass of water is 18.0 g/mol. Assume that water vapor can be treated as an ideal gas.)