5. A clay particle enters a current with a velocity of 0.25km/hour. If the grain is settling at a rate of 0.0025 cm/sec, how far from the coast will this grain travel before exiting the current (200 m)?

Solution: d=r t

0.0025 cm/sec x 3600 sec/hr = 0.09 m/hr

t=d/r = 200 m/ 0.09 m/hr =____ hr

d=r t = 0.25 km/hr x ____ hr

6. By analyzing samples from all the major rivers, we know that an element (x) enters the ocean at a rate of 7x10¹²g/yr. Measurements in hydrothermal systems show that the same element is added at 5x10¹¹g/yr. If the average concentration of the element in seawater is 1 mg/liter, what is the residence time of this element? Is it conservative or non-conservative?

Volume of the ocean. V_o = 1400 x10¹⁸liters

Solution: T_R = M_x / i_x

Compute input flux (rate)

i_x = i_x-r + i_x-h = 7x10¹²g/yr + 5x10¹¹g/yr= 7.5 x10¹²g/yr

Compute total mass

M_x = c_x V_o = 0.001g/l x 1400 x 10¹⁸l = 140 x 10¹⁶g

Substitute

T_R = M_x / i_x = 1.4 x 10¹⁸g / 7.5 x10¹²g/yr = 186,666 yr

This is a non-conservative element.

7. How much energy (kcal) is required to raise the temperature of 2000 liters of water from freezing to 20°C?

Solution:

I_H20= 1 cal/g/°C, m= 2000 liters = 2000 kg, ∆ T=20°C

E = ∆T m I

= (20°C) (2000 kg)(1 cal/g/°C)

= 40,000 kcal

8. How much heat (kcal) is required (per m²) to evaporate a 1 mm thick layer of seawater?

Solution: H = m x LH _evap

LH _evap = 540 cal/g, m=??

100 cm x 100 cm x 0.1 cm=1,000 cc = 1000 g

H = m x LH _fusion =1000g x 540 cal/g = 540,000 cal = 540 kcal