Consider a particular example of a lava flow with a volume of 5.2 × 10 7 m3and a

Question

Consider a particular example of a lava flow with a volume of 5.2 × 107m3and a density of 2.7 × 103kg m–3
which erupts at a temperature, Teropt, 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 × 103J kg–1°C–1, and that the average specific latent heat, L, released from the lava in solidifying into a crystalline rock is

4 × 105J 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

The volume of the lava is V = 5.2*107 m3 The density of the lava is = 2.7*103 kg/m3 The initial temperature Terr = 1145 oC The final temperature is Tf = 10 oC The specific heat of lava and rock is C = 1.5*103 J/kg-oC The latent heat of crystallisation is L = 4*105 J/kg a) The mass of the lava is m = V                                        = (5.2*107 m3)(2.7*103 kg/m3)                                        = 1.4*1011 kg b) The heat evolved when the lava at 1145 oC is colled to a temperature 10 oC is give by Q1 = mC(Tf -Terr) The heat evolved when the cooled lava at 10 oC is solidified to rock at 10 oC is given by Q2 = mL The total heat evoved is Q = mC(Tf -Terr) - mL c) The total heat evoved is Q = m{C(Tf -Terr) - L}     = (1.4*1011 kg){(1.5*103 J/kg-oC)(1145 oC - 10 oC) - 4*105 J/kg}     = -2.94*1017 J negative sign indicates that the heat is evolved The initial temperature Terr = 1145 oC The final temperature is Tf = 10 oC The specific heat of lava and rock is C = 1.5*103 J/kg-oC The latent heat of crystallisation is L = 4*105 J/kg a) The mass of the lava is m = V                                        = (5.2*107 m3)(2.7*103 kg/m3)                                        = 1.4*1011 kg b) The heat evolved when the lava at 1145 oC is colled to a temperature 10 oC is give by Q1 = mC(Tf -Terr) The heat evolved when the cooled lava at 10 oC is solidified to rock at 10 oC is given by Q2 = mL The total heat evoved is Q = mC(Tf -Terr) - mL c) The total heat evoved is Q = m{C(Tf -Terr) - L}     = (1.4*1011 kg){(1.5*103 J/kg-oC)(1145 oC - 10 oC) - 4*105 J/kg}     = -2.94*1017 J negative sign indicates that the heat is evolved Q2 = mL The total heat evoved is Q = mC(Tf -Terr) - mL c) The total heat evoved is Q = m{C(Tf -Terr) - L}     = (1.4*1011 kg){(1.5*103 J/kg-oC)(1145 oC - 10 oC) - 4*105 J/kg}     = -2.94*1017 J negative sign indicates that the heat is evolved Q = mC(Tf -Terr) - mL c) The total heat evoved is Q = m{C(Tf -Terr) - L}     = (1.4*1011 kg){(1.5*103 J/kg-oC)(1145 oC - 10 oC) - 4*105 J/kg}     = -2.94*1017 J negative sign indicates that the heat is evolved The total heat evoved is Q = m{C(Tf -Terr) - L}     = (1.4*1011 kg){(1.5*103 J/kg-oC)(1145 oC - 10 oC) - 4*105 J/kg}     = -2.94*1017 J negative sign indicates that the heat is evolved Q = m{C(Tf -Terr) - L}     = (1.4*1011 kg){(1.5*103 J/kg-oC)(1145 oC - 10 oC) - 4*105 J/kg}     = -2.94*1017 J negative sign indicates that the heat is evolved

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