Answer to Question #344827 in Molecular Physics | Thermodynamics for rox

Question

A 7.70-kg steel ball at 18.7°C is dropped from a height of 12.7 m into an insulated container with 4.50 L of water at 10.1°C. If no water splashes, what is the final temperature of the water and steel? The specific heat of steel and water is 450 J/(kg·K) and 4186 J/(kg·K) respectively.

Answer 1

$c_1m(t_1-t)+mgh=c_2\rho V(t-t_2),\implies$

$t=\frac{c_1mt_1+mgh+c_2\rho Vt_2}{c_1m+c_2\rho V}=11.5°C.$