Can someone check my answer for me...
1)Suppose a piece of lead with a mass of 14.9 g at a temperature of 92.5 degrees is dropped into an insulated container of water. The mass of water is 165 g and its temperature before adding the lead is 20.0 degrees. What is the final temperature of the system?
Answer: 20.19 degrees
You can find the specific heat of lead (C1) here:
http://www.sciencebyjones.com/specific_heat1.htm
The specific heat of water is
C2 = 1.000 Cal/g C
Set the heat gained by the water equal to the heat lost by the lead:
M1*C1*(92.5 - T)
= M2*C2*(T-20.0)
Now plug in the appropriate values for the masses M and the specific heats C, and solve for T.
M1 = 14.9 g
M2 = 165 g
To check your answer, we need to use the principle of conservation of energy. The energy gained by the water and lead must equal the energy lost by the lead.
First, calculate the energy gained by the water. The specific heat capacity of water is approximately 4.18 J/g°C.
The initial energy of the water is given by:
Energy_water_initial = mass_water * specific_heat_water * (final_temperature_water - initial_temperature_water)
= 165 g * 4.18 J/g°C * (T - 20.0°C)
Next, calculate the energy gained by the lead. The specific heat capacity of lead is approximately 0.13 J/g°C.
The initial energy of the lead is given by:
Energy_lead_initial = mass_lead * specific_heat_lead * (final_temperature_lead - initial_temperature_lead)
= 14.9 g * 0.13 J/g°C * (T - 92.5°C)
Lastly, since energy is conserved, the energy gained by the water and lead must equal the energy lost by the lead.
Therefore, we have the equation:
Energy_water_initial + Energy_lead_initial = 0
165 g * 4.18 J/g°C * (T - 20.0°C) + 14.9 g * 0.13 J/g°C * (T - 92.5°C) = 0
Now, solve this equation for T, the final temperature of the system.
165 g * 4.18 J/g°C * T - 165 g * 4.18 J/g°C * 20.0°C + 14.9 g * 0.13 J/g°C * T - 14.9 g * 0.13 J/g°C * 92.5°C = 0
Multiply the coefficients and constants:
689.7 T - 3309 gJ + 1.937 T - 180.6725 gJ = 0
Combine like terms:
691.637 T - 3489.67 gJ = 0
Divide both sides by g to get the result in degrees Celsius:
691.637 T - 3489.67 = 0
Solve for T:
691.637 T = 3489.67
T ≈ 3489.67 / 691.637
T ≈ 5.0455
Therefore, the final temperature of the system is approximately 5.05°C.
Comparing this with your answer of 20.19°C, it seems there might have been a calculation error in your answer. Please double-check your calculations.