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Q31. If 1L of water at pH 7 is mixed with 1L of water at pH 6, the resulting pH is:
[H+] of mix = (10^-7 + 10^-6)/2 = 5.5 x 10^-7. pH = -log(5.5 x 10^-7) = 6.26.
Q32. If the lowest Digital Number (DN) in a 10-bit image is 0, the maximum DN is:
10-bit resolution means 2^10 levels. 2^10 = 1024. Range is 0 to 1023.
Q33. Calculate bulk partition coefficient if Modes: 10% M1 (Kd=1.5), 40% M2 (Kd=1), 50% M3 (Kd=0.5).
Bulk Kd = Sum(Mode * Kd) = (0.1*1.5) + (0.4*1) + (0.5*0.5) = 0.15 + 0.4 + 0.25 = 0.8.
Q34. Calculate the concentration (in ppm) of Ni in olivine that crystallizes from a basaltic magma containing 20 ppm Ni. The partition coefficient (solid/melt) of nickel is 5.
Concentration in Solid = Partition Coefficient * Concentration in Liquid. C_solid = 5 * 20 = 100 ppm.
Q35. Specific discharge of 1 cm per day is observed in a porous medium where hydraulic head difference is 0.5 m and flow length is 20 m. Calculate the hydraulic conductivity (in m/day).
Darcy's Law: q = K(dh/dl). 0.01 m/day = K * (0.5/20). K = 0.01 / 0.025 = 0.4 m/day.
Q36. Normal fault dip 60E. Heave 5m, Throw 12m. Strike-slip 13m. True displacement is:
Dip-slip = sqrt(5^2+12^2) = 13m. Net slip = sqrt(Dip-slip^2 + Strike-slip^2) = sqrt(13^2 + 13^2) = 18.38m.
Q37. A watershed has area 74 km2. Stream lengths: 1st order=19.5km, 2nd order=32km, 3rd order=30km. Drainage density is (km/km2):
Drainage Density = Total Stream Length / Basin Area = (19.5 + 32 + 30) / 74 = 81.5 / 74 = 1.10.
Q38. A Wenner array with 60 m spacing between current electrodes (total length L=3a) is placed over inhomogeneous ground. Measured V=10 mV, I=5 mA. Calculate apparent resistivity (ohm-m). (Note: Wenner spacing 'a' is L/3 = 20m).
For Wenner array, Rho = 2 * pi * a * (V/I). Spacing a = 60/3 = 20m. Rho = 2 * 3.14 * 20 * (10/5) = 125.6 * 2 = 251.2 ohm-m.
Q39. If tangent Young's modulus (60 GPa) and modulus ratio (500) are given, the uniaxial compressive strength (MPa) is:
Modulus Ratio = Young's Modulus / UCS. Therefore, UCS = E / Ratio = 60,000 MPa / 500 = 120 MPa.
Q40. A sample contains 7 wt% CaO and 5 wt% MgO. The molar ratio of CaO to MgO is:
Moles = Wt% / Molar Mass. CaO (56 g/mol): 7/56 = 0.125. MgO (40 g/mol): 5/40 = 0.125. Ratio = 0.125/0.125 = 1.