We can calculate the final temperature of the metal and water mixture by equating the heat lost by the silver pellets to the heat gained by the water. We can use the formula q = m * c * ΔT and rearrange the equation to solve for the final temperature.
To solve this problem, we can use the principle of conservation of energy. The heat lost by the silver pellets will be equal to the heat gained by the water. We can use the formula:
q = m * c * ΔT
where:
q is the heat 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)
Let's calculate the heat lost by the silver pellets:
q_silver = m_silver * c_silver * ΔT_silver
Given that the mass of the silver pellets is 5.00 g and the change in temperature is the final temperature of the mixture minus the initial temperature of the silver pellets (T_final - 95.0°C), we can substitute the values into the equation.
Next, let's calculate the heat gained by the water:
q_water = m_water * c_water * ΔT_water
Given that the mass of the water is 97.3 g and the change in temperature is the final temperature of the mixture minus the initial temperature of the water (T_final - 22.0°C), we can substitute the values into the equation.
Since the heat lost by the silver pellets is equal to the heat gained by the water (q_silver = q_water), we can set up the equation:
m_silver * c_silver * ΔT_silver = m_water * c_water * ΔT_water
Now, we can rearrange the equation to solve for the final temperature of the mixture (T_final):
T_final = (m_silver * c_silver * ΔT_silver + m_water * c_water * ΔT_water) / (m_silver * c_silver + m_water * c_water)
By plugging in the given values and solving the equation, we can find the final temperature of the metal and water mixture.