A27.5 −g aluminum block is warmed to 65.9 ∘c and plunged into an insulated beaker containing 55.5 g water initially at 22.1 ∘c. the aluminum and the water are allowed to come to thermal equilibrium. assuming that no heat is lost, what is the final temperature of the water and aluminum?

The final temperature of aluminium ≈ 26.32 °C

Explanation:

Step 1: explain the problem

A 27.5 −g aluminum block is warmed to 65.9 ∘C and plunged into an insulated beaker containing 55.5 g water initially at 22.1 ∘C.

Step 2: Data given

We will use the formule : Q = mcΔT

with Q = heat transfer ( J)

with m = mass of the substance (g)

with c = specific heat ( J/g °C)

with ΔT = change in temperature ( in °C or K)

mass of aluminium = 27.5g

mass of water = 55.5g

specific heat of aluminium = 0.900J/g °C

specific heat of water = 4.186 J/g °C

initial temperature of aluminium T1= 65.9 °C

initial temperature of water T1 =  22.1 °C

final temperature of water and aluminium = TO BE DETERMINED

Step 3: Calculate the initial temperature

To find the final temperature, we have to use the  following formule:

-(Mass of aluminium) * (caluminium)*(ΔT)) = (Mass of water) *(cwater)*(ΔT)

-27.5g (0.900)(T2 - 65.9) = 55.5g (4.184j/g °C) (T2- 22.1)

-24.75*(T2-65.9) = 232.212 *(T2-22.1)

-24.75T2 + 1631.025 = 232.212T2 -5131,8852

-256.962 T2 = -6762.9102

T2 = 26.32 °C

The final temperature of aluminium ≈ 26.32 °C

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3