Difficult# Final Temperature of Hot Bath Ice Mixture

APPH12-VAI3NU

After a long, hard day of school, you settle into your bathtub for a good soak to relieve stress. Your younger brother runs in with a bucket of cold water and dumps it in the tub.

The tub is full of hot water ($T={ 45 }^{ \circ }\text{C}$) prior to you entering and has dimensions of $1.5\ \text{m}$ by $0.5\text{ m}$ by $0.5\text{ m}$. The cold water has a mass of $10\text{ kg}$ and a temperature of $T={ 4 }^{ \circ }\text{C}$.

What is the final equilibrium temperature of the mixture?