In an experiment 50 g of a metal was heated to 100oC and placed in 200 g of a liquid at 25oC. Which of the following combinations of metal and liquid will produce the largest temperature increase in the liquid? (Assume that there is no energy transfer to the surroundings.)

Question

Choose one answer.
a. Al, C2H5OH
b. Au, H2O
c. Cu, CCl2F2
d. Fe, CCl4

Answer 1

Lets look at the math.

Sum of heats gained is zero.
50*Cmetal(Tf-100)+200*Cliquid(Tf-25)=0

Tf(50Cmetal+200Cliquid)=200Cliquid*25+5000Cmetal

Tf=(200Cliquid+5000Cmetal)/(50Cmetal+200Cliquid)
multiplying the right side numerator and deoominator by 1/cliquid

Tf=(200+5000cm/cl)/(50cm/cl+200)

let cm/cl be x.

well, it is apparent to me that the cm/cl term in the numerator predominates, so it needs to be maximized .

So the metal with the largest specific heat, and the liquid with the least.

so on the four choices, compute cm/cl . the winner is the highest ratio.