We know that in such interactions heat is gained by one and heat is lost is by the other.
Also that the heat gained/lost is given by
In the given problem heat is lost by steam to condense and gained by ice which melts.
When ice melts first it becomes water at
For sake of this problem, heat of melting of ice is being equated with heat of condensation of steam, i.e., change of phase in both cases. Latent heat for condensation of water is
- Heat released by condensation of steam
- Heat required to melt ice
Equating both we get