Consider a particular example of a lava flow with a volume of 5.2 x 10 7 m 3 and
ID: 10889 • Letter: C
Question
Consider a particular example of a lava flow with a volume of 5.2 x 107 m3 and a density of 2.7 x 103 kg m-3 which erupts at a temperature , Terupt , of 1145o C and cools to a final temperature, Tfinal, of 10o C. Assume that the specific heat capacity ,c, of both the lava and the rock formed is 1.5 x 103 J kg-1 o C-1, and that the average specific latent heat ,L, released from the lava in solidifying into a crystalline rock is 4 x 105 J kg -1.
(i) calculate the mass,m, of lava (showing all workings)
(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 he total amount of energy,q, releaed by the lava. (show all workings)
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 evolved 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 here negative sign indicates that the heat is evolved 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 evolved 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 here 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 evolved 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 here negative sign indicates that the heat is evolved Q2 = mL The total heat evoved is Q = mC(Tf -Terr) - mL (c) The total heat evolved 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 here negative sign indicates that the heat is evolved Q = mC(Tf -Terr) - mL (c) The total heat evolved 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 here negative sign indicates that the heat is evolved The total heat evolved 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 here 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 here negative sign indicates that the heat is evolvedRelated Questions
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