A 12 gram piece of Cu at 475 oC is placed in contact with a 15 gram piece of Cr at 265 oC. Assume the two pieces of metal are the system and that there is no heat exchange between system and surrounding.

What is the final temperature of the two pieces of metal expressed in degree C?

349.22°C

Explanation:

Let the final temperature of the two pieces of metal be x.

Now, the warmer metal which is C u reduces from 475°C to x. Thus Δt for C u is; Δt1 = 475 - x.

The cooler metal Cr increases in temperature from 265°C to x. Thus, it's change in temperature is Δt for Cr is; Δt2 = x - 265.

Now from conservation of energy, the amount of energy leaving the C u metal is equal to the amount of energy entering the Cr metal.

Thus;

q_lost = q_gain

Where;

q_lost = m1•c1•Δt1

q_gained = m2•c2•Δt2

Now, c1 & c2 are the specific heat capacity of C u and Cr respectively.

From online tables, c1 = 0.385 J/g°C and c2 = 0.46 J/g°C

We are given;

m1 = 12g and m2 = 15g

Thus;

12 × 0.385 × (475 - x) = 15 × 0.46 × (x - 265)

2194.5 - 4.62x = 6.9x - 1828.5

6.9x + 4.62x = 2194.5 + 1828.5

11.52x = 4023

x = 4023/11.52

x = 349.22°C