Solve Latent Heat Problem: Mass of Injected Steam

[dolerka]

Homework Statement

Steam at 100°C is injected into 1.8 kg of water at 22°C in a well-insulated container, where it condenses and mixes with the existing water, reaching thermal equilibrium. If the final temperature of the well-mixed water is 25°C, what is the mass of the injected steam?

Latent heat of vaporization of water, L_v=2.26e6

Homework Equations

Q = cmΔT, equation for specific heat. specific heat constant c=4178
Q=L_vm, equation for energy of vaporization, m=mass.

The Attempt at a Solution

I first stated that since the the steam is losing energy during its phase change it is negative, -Q_p.-Q_p=L_vm_s
The amount of energy for the temperature change of the steam.
Q_s=cm_sdT_s
Q_s=(4178)m_s(22-100)
The amount of energy for the temperature change of the water.
Q_w=cm_wdT_w
Q_w=(4178)(1.8)(25-22)

I know i need arrange together in someway but I am just a little confused on that part.

 

[rl.bhat]

Heat gained by the water Qw=(4178)(1.8)(25-22)

Heat lost by the steam Qs = Lv*ms + (4178)*ms*(100 - 25)