To find the final temperature of the water and metal, we can use the principle of heat transfer, which states that the heat lost by the metal is equal to the heat gained by the water.
The heat lost by the metal can be calculated using the formula:
Q_lost = m * c * ΔT
where:
m is the mass of the metal (in grams)
c is the specific heat capacity of the metal (in J/(g°C))
ΔT is the change in temperature of the metal (final temperature - initial temperature)
Similarly, the heat gained by the water can be calculated using the formula:
Q_gained = m * c * ΔT
where:
m is the mass of the water (in grams)
c is the specific heat capacity of water (4.18 J/(g°C))
ΔT is the change in temperature of the water (final temperature - initial temperature)
Since the heat lost by the metal is equal to the heat gained by the water, we can set up the equation:
m_metal * c_metal * ΔT_metal = m_water * c_water * ΔT_water
Substituting the given values:
m_metal = 10.0 g
c_metal = 0.451 J/(g°C)
ΔT_metal = final temperature of the metal - initial temperature of the metal (80°C - final temperature of the metal)
m_water = 70 g
c_water = 4.18 J/(g°C)
ΔT_water = final temperature of the water - initial temperature of the water (final temperature of the water - 25°C)
Simplifying the equation, we have:
10.0 * 0.451 * (80 - final temperature of the metal) = 70 * 4.18 * (final temperature of the water - 25)
Solving this equation will give us the final temperature of the metal and the final temperature of the water.