Find an expression for the isothermal compressibility thermal expansion for a va

Question

Find an expression for the isothermal compressibility thermal expansion for a van der Waals gas. The virial equation of state for a fluid is given to second order by: PV = RT {1 + B/V} where B is in general a function of T, i.e. B = B(T). Find the isothermal compressibility for a fluid obeying this equation of state. For certain gases it may be shown that B(T) = e - g/T. Using the result in part a), find the highest temperature at which the gas may be liquefied. Global warming will result in a rise in the average sea level. A large part of this is the caused by thermal expansion of the world's oceans due to rising average temperatures (the other part is melting of the polar glaciers, which will add about 1 m). The average depth (h) of oceans is 4000 meters, and the radius of the earth is 6370 km. The coverage of earth by oceans is about 70%. The coefficient of thermal expansion for H_2O is 2.1 times 10^-4 C^-1. By 2050 the average temperature of the earth is expected to rise by about 3^0C. Calculate the increase in sea level by 2050. Calculate cx and k_T for ideal gas as well

Explanation / Answer

The area of the earth will be = 4*pi*r2 = 7.2843*1014 m2
Out of which 70% is water, 0.7 * 7.2843*1014 m2 = 5.09904*1014 m2 (occupied by water)
Thermal coeffcient of expanison of water is 2.1*10-4 C-1 which means that 2.1 * 10-4 m2 (size)
will expand for every 1oC rise
for 3oC rise, 3 * 2.1*10-4 = 6.3*10-4 m
melting of polar glaciers will add 1m
By 2050 globally sea level may rise upto = 6.3*10-4 m + 1m = 1.00063 m

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