The value of specific heat for copper is 390 J/kg⋅C∘, for aluminun is 900 J/kg⋅C∘, and for water is 4186 J/kg⋅C∘.What will be the equilibrium temperature when a 275g block of copper at 255∘C is placed in a 145g aluminum calorimeter cup containing 855g of water at 12.0∘C?

To find the equilibrium temperature, we need to understand the concept of heat transfer. When two substances at different temperatures come into contact, heat is transferred from the hotter substance to the cooler substance until they reach thermal equilibrium, where their temperatures are equal.

In this problem, the copper block and aluminum calorimeter cup will exchange heat until reaching equilibrium, and then the water in the calorimeter will also reach the same equilibrium temperature. We can use the principle of conservation of energy to determine this equilibrium temperature.

First, let's calculate the heat transferred from the copper block to the aluminum cup using the equation:

Q1 = m1 * c1 * ΔT1

where:
Q1 is the heat transferred from the copper block to the aluminum cup,
m1 is the mass of the copper block,
c1 is the specific heat of copper,
and ΔT1 is the change in temperature of the copper block.

Q1 = 275g * 390 J/kg⋅C∘ * (T1 - 255∘C)

Now, let's calculate the heat transferred from the aluminum cup to the water using the equation:

Q2 = m2 * c2 * ΔT2

where:
Q2 is the heat transferred from the aluminum cup to the water,
m2 is the mass of the water,
c2 is the specific heat of water,
and ΔT2 is the change in temperature of the water.

Q2 = 855g * 4186 J/kg⋅C∘ * (T2 - 12.0∘C)

Since heat is conserved, the heat transferred from the copper block to the aluminum cup is equal to the heat transferred from the aluminum cup to the water. Therefore, we can equate Q1 and Q2:

275g * 390 J/kg⋅C∘ * (T1 - 255∘C) = 855g * 4186 J/kg⋅C∘ * (T2 - 12.0∘C)

Now, let's solve this equation to find the equilibrium temperature (T2).