Suppose a piece of lead with a mass of 14.9g at a temperature of 92.5c is dropped into an insulated container of water. The mass of water is 165g and its temperature before adding the lead is 20.0c. What is the final temperature of the system?
The sum of the heats gained is zero (some will absorb heat)
Heatgainedlead + heatgained water=0
ml*cl*(Tf-92.5) + mw*Cw*(Tf-20)=0
solve for Tf.
i don't understand
To calculate the final temperature of the system, you need to use the principle of conservation of energy. This principle states that the sum of the heat gained and the heat lost in a system is equal to zero.
In this case, the lead loses heat and the water gains heat as they come into thermal contact. The amount of heat gained or lost can be calculated using the equation Q = m * c * ∆T, where Q is the heat gained or lost, m is the mass, c is the specific heat capacity, and ∆T is the change in temperature.
The heat gained by the lead can be calculated as Q_lead = m_lead * c_lead * (∆T_lead), where m_lead is the mass of the lead, c_lead is the specific heat capacity of lead, and (∆T_lead) is the change in temperature of the lead.
Similarly, the heat gained by the water can be calculated as Q_water = m_water * c_water * (∆T_water), where m_water is the mass of the water, c_water is the specific heat capacity of water, and (∆T_water) is the change in temperature of the water.
Since the sum of the heat gained and the heat lost is zero, we can set up the equation as follows:
Q_lead + Q_water = 0
m_lead * c_lead * (∆T_lead) + m_water * c_water * (∆T_water) = 0
Now, substitute the values given in the problem:
m_lead = 14.9g, c_lead = specific heat capacity of lead, (∆T_lead) = final temperature - 92.5°C
m_water = 165g, c_water = specific heat capacity of water, (∆T_water) = final temperature - 20.0°C
The unknown value is the final temperature (Tf) of the system. Rearrange the equation to solve for Tf:
m_lead * c_lead * (∆T_lead) + m_water * c_water * (∆T_water) = 0
(14.9g) * (specific heat capacity of lead) * (Tf - 92.5°C) + (165g) * (specific heat capacity of water) * (Tf - 20.0°C) = 0
Solve this equation for Tf to find the final temperature of the system. Note that you will need to know the specific heat capacities of lead and water to get an exact value for Tf.