Question

Lava at T_H = 950° C emerges from a volcano. A mass m = 95 kg of this lava flows at a constant velocity of v = 0.45 m/s losing Q = 14000 J of heat every second to the surroundings. The lava flows a distance of 250 m before reaching the ocean.

Assume that the temperature of the surroundings, T_surr = 23° C is unaffected by the cooling of the lava.

a)  Calculate how long t in seconds it takes before this mass of lava reaches the ocean.

b)  Calculate the amount of heat Q_l in joules lost to the surroundings before this mass reaches the ocean.

c) If the specific heat capacity of the lava in this process is c = 840 J / kg °C, calculate the temperature of this mass of lava T in celsius just before it reaches the ocean.

d) Calculate entropy change of the surroundings ΔS_surr in J / K while the lava was moving toward the ocean.

e) Calculate the change in the entropy of the lava ΔS in joules per kelvin while the lava was moving toward the ocean.

Answer 1

a) Distance covered by lava to reach the ocean, d = 250 m

Lava is flowing with constant velocity, v = 0.45 m/s

So, the time taken by the lava to reach the ocean is,

b) The lava loses Q = 14000 J of heat every second to the surroundings.

So, it loses 14000 J heat in 1 s.

Thus, in 555.56 s, it will lose 14000* 555.56 J = 7777840 J of heat to the surroundings before it reaches the ocean.

c) The formula for the specific heat capacity can be written as

  

where = the change in thermal energy

m = mass of substance = 95 Kg

c = specific heat capacity = c = 840 J / kg °C

   = change in temperature

Amount of heat lose by lava = 7777840 J So, = -7777840 J

Let the final temperature of the lava just before it reaches the ocean be T.

So, = Tfinal - Tinitial = T - 950° C

Put all these values in above equation,

  

d) As the temperature of the surroundings, Tsurr = 23° C is unaffected by the cooling of the lava. thus, there is no change in entropy of the surroundings.

e) The entropy change of lava can be given as

  

  

  

  

Here 840 is divided by 274.15 to convert it from J / kg °C to J / kg K.