Question

How would you make a chocolate clam soup served at body temperature?What temperature should the clams start at so that the soup reaches a perfect serving temperature of 37.0^oC?

Liquid chocolate specific heat capacity-1.60J/g^oC

80.0g chocolate at 45.0^oC

Clam specific heat capacity-3.52J/g^oC

20g clams

Answer 1

Given: Mass of liquid chocolate = 80.0g
   Specific heat capacity of liquid chocolate = 1.60 J/g℃
   Initial temperature of the liquid chocolate = 45.0 ℃
   Final temperature of the liquid chocolate = 37.0 ℃
   Mass of clam = 20 g
Specific heat capacity of clam = 3.52 J/g℃
Final temperature of clam = 37 ℃

Assuming that no heat is lost to the surroundings, we have

Heat gained by clam = Heat lost by liquid chocolate

Mass of clam x Specific heat capacity of clam x (Final temperature of clam - Initial temperature of clam) = Mass of liquid chocolate x Specific heat capacity of liquid chocolate x (Initial temperature of the liquid chocolate - Final temperature of the liquid chocolate)
⇒ 20 x 3.52 x (37 - Initial temperature of clam) = 80 x 1.60 x (45.0 - 37.0)
⇒ 37 - Initial temperature of clam = 14.55
⇒ Initial temperature of clam = 37 - 14.55
⇒ Initial temperature of clam = 22.45 ℃

Therefore, clam should start at 22.45 ℃.