Calculate the equilibrium temperature of the water.

Question

A 47.0g sample of brass, which has a specific heat capacity of 0.375·J·g−1°C−1, is dropped into an insulated container containing 300.0g of water at 15.0°C and a constant pressure of 1atm. 

The initial temperature of the brass is 83.3°C.

Assuming no heat is absorbed from or by the container, or the surroundings, calculate the equilibrium temperature of the water.

Be sure your answer has the correct number of significant digits.

I'm having trouble finding the answer even when I use the formula, I think I'm messing up with the temperature, but I would appreciate seeing the process.

Answer 1

Heat lost by brass must equal heat gained by water

Heat lost by brass = q = mC∆T = (47.0 g)(0.375 J/gº)(83.3 - Tf) where Tf is final temperature of water

Heat gained by water = q = mC∆T = (300.0 g)(4.184 J/gº)(Tf - 15.0º)

Setting these two equal we have...

(47.0 g)(0.375 J/gº)(83.3 - Tf) = (300.0 g)(4.184 J/gº)(Tf - 15.0º)

1469 - 17.6Tf = 1255Tf - 18,828

1273Tf = 20297

Tf = 15.9ºC = equilibrium temperature of water

Answer 2

Hi, Abigail,

I couldn't fit my table within the space limitations. I loaded it to: https://docs.google.com/spreadsheets/d/1I6M7PTs3GvKax6H69SrKDNABdb8bqoigA_hHxmVg01Y/edit?usp=sharing

Work from the logic in the chart:

I didn't pay attention to sig figs, but I used 3 in the final answer of 16^oC, based on the 47.0C value.. Note that when heat is released, it is a positive value. The heat absorbed by water is shown as a negative, but numerically equal to that released by the brass. Problems with temperature arise either here or in the definition of temperature change (Dt = T1 - T2). I suspect one of these is the cause of your observation.

I was taken aback by how small the increase was, 0.96C. But it makes sense when you realize, from it's specific heat, what a heat-monger water is. A high heat capacity means it takes forever and a day for water to heat and boil. Brass, on the other hand, hates heat and will dispense what little it has, with relative little impact, unless it is my finger.

I hope this helps,

Bob