A 30.0 g sample of water at 280. K is mixed with 50.0 g of water at 330 K. Calculate the final temperature of the mixture assuming no heat loss to the surroundings. Remember that the heat gained by the cooler water is equal to the heat lost by the warmer water.

c = cool

w = warm
[mass w H2O x specific heat H2O x (Tfinal-Tinitial)] + [mass c H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Subsitute and solve for Tfinal.

To calculate the final temperature of the mixture, you can use the principle of conservation of energy. According to this principle, the heat gained by the cooler water is equal to the heat lost by the warmer water.

The heat gained or lost by an object can be calculated using the formula:

Q = mcΔT

Where:
Q is the heat gained or lost (in units of energy, usually Joules)
m is the mass of the object (in kilograms)
c is the specific heat capacity of the substance (in units of energy per mass per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)

Let's start by calculating the heat lost by the warmer water.

Heat lost by the warmer water (Q1) = m1 * c1 * ΔT1

m1 = mass of the warmer water = 50.0 g = 0.050 kg
c1 = specific heat capacity of water = 4.18 J/g°C (or 4180 J/kg°C, since 1 g = 0.001 kg)
ΔT1 = change in temperature of the warmer water = final temperature - initial temperature = Tfinal - 330 K

Now, let's calculate the heat gained by the cooler water.

Heat gained by the cooler water (Q2) = m2 * c2 * ΔT2

m2 = mass of the cooler water = 30.0 g = 0.030 kg
c2 = specific heat capacity of water = 4.18 J/g°C (or 4180 J/kg°C, since 1 g = 0.001 kg)
ΔT2 = change in temperature of the cooler water = final temperature - initial temperature = Tfinal - 280 K

Since the heat lost by the warmer water is equal to the heat gained by the cooler water, we can set up an equation:

Q1 = Q2

m1 * c1 * ΔT1 = m2 * c2 * ΔT2

Substituting the given values:

0.050 kg * 4180 J/kg°C * (Tfinal - 330 K) = 0.030 kg * 4180 J/kg°C * (Tfinal - 280 K)

Now we can solve this equation to find the final temperature (Tfinal) of the mixture.