PLEASE HELP OR I WILL FAIL
What would be the final temperature of the system if 16.6 g of lead at 138 ◦C is dropped into 23.4 g of water at 8.68 ◦C in an insulated
container? The specific heat of lead is 0.128J/g◦C.
The sum of the heats gained is zero? (some gain, some lose)
HeatgainedbyWater+heatgainedbylead=0
23.4*Cw*(Tf-8.68)+16.6*cpb*(Tf-138)=0
look up the specific heats for water, and lead, then solve for Temp final Tf
To determine the final temperature of the system, you can use the principle of conservation of energy, specifically the heat transfer equation:
q_lead + q_water = 0
Where q_lead is the heat gained/lost by the lead, and q_water is the heat gained/lost by the water.
The heat gained/lost by a substance can be calculated using the formula:
q = m * c * ΔT
Where q represents the heat gained/lost, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, we can calculate the heat gained/lost by the lead and the water separately and set the total heat equal to zero.
1. Calculating the heat gained/lost by the lead:
q_lead = m_lead * c_lead * ΔT_lead
Given:
m_lead = 16.6 g
c_lead = 0.128 J/g◦C
ΔT_lead = final temperature - initial temperature
The initial temperature of the lead is 138 ◦C, and we want to find the final temperature of the system.
2. Calculating the heat gained/lost by the water:
q_water = m_water * c_water * ΔT_water
Given:
m_water = 23.4 g
c_water = specific heat capacity of water (approximated as 4.18 J/g◦C)
ΔT_water = final temperature - initial temperature
The initial temperature of the water is 8.68 ◦C, and we want to find the final temperature of the system.
3. Setting the total heat equal to zero:
q_lead + q_water = 0
Substituting the formulas from steps 1 and 2:
m_lead * c_lead * ΔT_lead + m_water * c_water * ΔT_water = 0
Now you can solve this equation to find the final temperature of the system. Rearrange the equation to isolate the final temperature term and plug in the given values.
Solving the equation will give you the final temperature of the system.