The Three-dimensional Temperature Distribution and its Variation in Time 125 



h^ can be calculated using a formula derived from the energy principle by Lord Kelvin j 

 v^'hich in c.g.s. -units take the form: 



''" Ta*g 



8& 



r dz, 



hi ^v' 



where T is the absolute temperature of the water, a* is its coefficient of thermal ex- 

 pansion, Cp is the specific heat at constant pressure, g is the gravitational acceleration 

 and J is the mechanical equivalent of heat (4-1863 x 10' erg/cal). 



The adiabatic temperature change hd for a displacement from a depth h^ to a depth 

 //o is thus dependent on the coefficient of thermal expansion and on the specific heat 

 of sea-water, which are both effectively dependent on the temperature, the salinity 

 and the pressure (see p. 49). 



After solving the above equation, Ekman (1914) has presented numerical values 

 which allow an easy determination of the adiabatic effects for sea-water. Helland- 

 Hansen (1930) later prepared from these values tables giving directly the adiabatic 

 heating and cooling in sea-water of o^ = 28-0 (corresponding to a salinity of 34'85%o) 

 when raised from a given depth to the surface with a given temperature; a further 

 table gives the adiabatic temperature change for the upper 100 m for salinities be- 

 tween 30-0%o and 38-0%o. With these tables or the corresponding diagrams, any adia- 

 batic change can be determined without difficulty. Table 52 is extracted from these 

 tables. 



Example: at a depth of 9788 m (Philippine Trench) a temperature of 2-60° C was 

 measured and a density o- = 28. What would be the temperature of the water for an 

 adiabatic ascent to the surface? Table 52 gives, by interpolation, a T-change at 2-60° 

 of — M37°C for 9000 m; for 10,000 m the change would be —1-319° and this for 

 9788 m —1 -280-0. If the water at 9788 m rises to the surface there will be an adia- 

 batic temperature change from 2-60°C to 1-32°C. 



The temperature of a water mass after being moved adiabatically to the surface 

 is known as the potential temperature. It is given hy d = d -\- 8§. If the vertical 

 stratification of the sea were such that the salinity were constant, so that the density 

 would only depend on the temperature, then the equilibrium state ofthe sea could be 

 shown by the vertical distribution of the potential temperature in the same way as in the 

 atmosphere. Complete mixing of the water masses in vertical direction would eliminate 



t This above equation can be derived without difficulty from the first and second laws of thermo- 

 dynamics. If the state of a body is defined as a function of the temperature T and the pressure p, 

 then 



T da 

 dQ = c,dT-j^dp. 



Taking the definition of the coefficient of thermal expansion (see p. 48) as 



1 da 

 -^ = «* 



a ct 



and the static equation as dp = gp dz then for an adiabatic process (dQ = 0) with pa = \ and 

 /& = JT 



8 »= f dz 



or for the interval from h^ — h^ the above formula is derived. 



