Mid-ocean ridges and other volcanic areas emit a large amount of energy due to t
ID: 2943313 • Letter: M
Question
Mid-ocean ridges and other volcanic areas emit a large amount of energy due to the cooling of magma. In this part of Question 5 you will calculate the amount of energy that could be obtained from this source. The answer will depend on how much lava there is, its initial temperature and its physical properties (such as specific heat capacity and the specific latent heat of solidification).
Consider a particular example of a lava flow with a volume of 5.2 × 10 to power 7 m3 and a density of 2.7 × 10 to power 3 kg m–3 which erupts at a temperature, Terupt, of 1145 °C and cools to a final temperature, Tfinal, of 10 °C. Assume that the specific heat capacity, c, of
both the lava and the rock formed is 1.5 × 10 to power 3 J kg–1 °C–1, and that the average specific latent heat, L, released from the lava in solidifying into a crystalline rock is 4 × 10to power 5 J kg–1.
(i)
Calculate the mass, m, of lava. (Show all of your working.)
(ii)
Write an equation, using symbolic notation, expressing the total energy, q, released from the lava as a result of cooling and crystallisation.
(iii) Calculate the total amount of energy, q, released by the lava. (Show all of your working.)
Explanation / Answer
(i) M = p V where p = density and V the volume M = 5.2 * 10E7 m^3 * 2.7 * 10E3 = kg/m^3 = 1.4 * 10E11 kg (ii) Q = M Lf + c M (T2 - T1) where Q is heat lost by lava, Lf the latent heat of fusion and c the specific heat of lava - since the specific heat given is the same for the molten and solid lava we can use T2 - T1 = 1145 - 10 = 1135 regardless of the temperature at which fusion occurs (iii) Q = M [Lf + c (T2 - T1)] Q = 1.4 * 10E11 (4 * 10E5 + 1.5 * 10E3 * 1135) = 2.9 *10E17 J