Solving for the Final Temperature of a Mixture
What is the final temperature of the mixture?
227 g of lead shot at 116°C is mixed with 101.5 g of water at 66.3°C in an insulated container. How can we determine the final temperature of the mixture?
Calculation for the final temperature:
By applying the principle of conservation of energy and utilizing the formula for heat transfer, we can determine the final temperature of the lead shot-water mixture.
When two substances come into thermal contact, the heat obtained by one substance must equal the heat lost by the other substance. In this case, we have lead shot and water exchanging heat until they reach a final equilibrium temperature.
The formula for heat transfer (Q) is given by:
Q = m * c * ∆T
Where:
Q = heat transferred,
m = mass of the substance,
c = specific heat capacity of the substance,
∆T = change in temperature.
By equating the heat lost by the lead shot to the heat gained by the water, we can set up the equation:
m_lead * c_lead * ∆T_lead = -m_water * c_water * ∆T_water
Solving for the final temperature (T_final) of the mixture, we have:
T_final = (m_lead * c_lead * T_lead + m_water * c_water * T_water) / (m_lead * c_lead + m_water * c_water)
Given the specific values for lead shot and water, we substitute them into the equation and calculate T_final:
T_final ≈ 75.4 °C
Therefore, the final temperature of the lead shot-water mixture is approximately 75.4°C.