A silver cube with an edge length of 2.25 cm and a gold cube with an edge length of 2.63 cm are both heated to 81.6∘C and placed in 119.0 mL of water at 20.3 ∘C.

Question

substance	Specific heat (J/g·°C)Density (g/cm3)	density g/cm^3)
gold	0.1256	19.3
silver	0.2386	10.5
water	4.184	1.00

What is the final temperature of the water when thermal equilibrium is reached?

Answer 1

My approach is somewhat different from that provided by Dr. Bob. Here is the way I would approach this problem.

Heat lost by the hot gold + that lost by the hot silver must equal the heat gained by the cool water.

Heat lost or gained is q = mC∆T where m is the mass, C is the specific heat and ∆T is change in temperature.

Before applying this formula, we will first find the mass of the gold, silver and water.

mass of gold = (2.63 cm)3 x 19.3 g/cm3 = 351 g

mass of silver = (2.25 cm)3 x 11.39 g/cm3 = 120 g

mass of water = 119 ml x 1.00 g/ml = 119 g

heat lost by gold = (351 g)(0.1256 J/gº)(81.6 - Tf)

heat lost by silver = (120 g)(0.2386 J/gº)(81.6 - Tf)

heat gained by water = (119 g)(4.184 J/gº)(Tf - 20.3)

(351 g)(0.1256 J/gº)(81.6 - Tf) + (120 g)(0.2386 J/gº)(81.6 - Tf) = (119 g)(4.184 J/gº)(Tf - 20.3)

When I solve for Tf (final temperature) I get a value of 28.1ºC

You should go over this and do it yourself. Check my math please.

Answer 2

Hello, Bri,

Tough problem, and there isn't enough room here for my complete answer. Please follow my logic, rather than my calculations, since I'm not certain I approached it correctly. Calculate the masses for all components and use a weighted average of each and applied that to each substance's specific heat to arrive at a "system" specific heat. My logic was to calculate all the heat present in the the materials and then use the weighted specific heat to calculate the temperature rise based on c = q/mDT, where DT is (T1 - T2)

I can't load my calculations due to space constraints. My quick estimate for this approach was a temperature increase to 21.5C, but this is an estimate.

Good luck, Bob