determine the final temperature of a system after 100.0g of zinc ( specific heat .3876 J/g c) at 95.0 C is immersed into 50.0 g of water at 15.C

heat lost by Zn + heat gained by H2O = 0

[mass Zn x specific heat Zn x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Solve for Tf, the only unknown.

To determine the final temperature of the system, we can use the principle of conservation of energy. The energy gained by the water will be equal to the energy lost by the zinc. We can calculate the energy gained or lost using the formula:

q = m * c * ΔT

where:
q is the heat energy gained or lost (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g°C),
ΔT is the change in temperature (in °C).

First, let's calculate the amount of heat energy gained or lost by the zinc. The initial temperature of the zinc is 95.0°C, and we want to find the final temperature.

q_zinc = m_zinc * c_zinc * ΔT_zinc

m_zinc = 100.0 g (mass of zinc)
c_zinc = 0.3876 J/g°C (specific heat of zinc)
ΔT_zinc = Tf - Ti = Tf - 95.0°C (change in temperature of zinc)

Now, let's calculate the amount of heat energy gained or lost by the water. The initial temperature of the water is 15.0°C, and we want to find the final temperature.

q_water = m_water * c_water * ΔT_water

m_water = 50.0 g (mass of water)
c_water = 4.184 J/g°C (specific heat of water)
ΔT_water = Tf - Ti = Tf - 15.0°C (change in temperature of water)

Since the energy gained by the water is equal to the energy lost by the zinc, we can set up the equation:

q_zinc = -q_water

Now, substitute the values into the equations and solve for the final temperature, Tf:

m_zinc * c_zinc * (Tf - 95.0) = -m_water * c_water * (Tf - 15.0)

100.0 g * 0.3876 J/g°C * (Tf - 95.0) = -50.0 g * 4.184 J/g°C * (Tf - 15.0)

Simplify the equation:

38.76 Tf - 3678 = -209.2 Tf + 3144

Combine like terms:

38.76 Tf + 209.2 Tf = 3678 + 3144

247.96 Tf = 6822

Divide both sides by 247.96:

Tf ≈ 27.5°C

Therefore, the final temperature of the system is approximately 27.5°C.