A 150g piece of copper is heated to 100oC. It is then held in the open air for 2 minutes and 31 seconds, and then dropped into a 100g copper calorimeter containing 200g of water at 17oC. If the rate of loss of heat of the copper piece while held in the air is 12.6J/sec, determine the final equilibrium temperature.

To determine the final equilibrium temperature, we need to calculate the heat gained by the water and the calorimeter, as well as the heat lost by the copper piece. Then, we can equate the two to find the equilibrium temperature.

The heat gained by the water and calorimeter can be calculated using the formula:

Q = m * c * ΔT

where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Given:
Mass of water (m_w) = 200g
Specific heat capacity of water (c_w) = 4.18 J/(g°C)
Initial temperature of water (T_w, initial) = 17°C

Using the given values, we can calculate the heat gained by the water and calorimeter during the mixing process:

Q_w = m_w * c_w * ΔT_w
= 200g * 4.18 J/(g°C) * (T_f - T_w, initial)

Now, let's calculate the heat lost by the copper piece while held in the air. The rate of heat loss is given as 12.6J/sec, and the time is given as 2 minutes and 31 seconds.

Converting the time to seconds:
2 minutes = 2 * 60 seconds = 120 seconds
31 seconds = 31 seconds

Total time (t) = 120 seconds + 31 seconds = 151 seconds

Heat lost by the copper piece (Q_c) = rate of heat loss * time
= 12.6 J/sec * 151 seconds

Now, the heat lost by the copper piece during the mixing process is equal to the heat gained by the water and calorimeter:

Q_c = Q_w

Therefore, we can equate the two equations:

rate of heat loss * time = m_w * c_w * ΔT_w

Solving for the final equilibrium temperature (T_f):
T_f = (Q_c + Q_w) / (m_w * c_w) + T_w, initial

Substituting the values we've calculated, we can find the final equilibrium temperature.

To determine the final equilibrium temperature of the system, we can use the principle of conservation of energy. The heat lost by the copper piece in the air will be equal to the heat gained by the water and the calorimeter.

1. Calculate the heat lost by the copper piece in the air:
Heat lost = mass x specific heat capacity x change in temperature
= 0.15kg x 390J/kg oC x (100oC - room temperature)
(We assume room temperature is approximately 25oC)
= 0.15kg x 390J/kg oC x 75oC
= 2,925J

2. Calculate the heat gained by the calorimeter and water:
Heat gained = mass x specific heat capacity x change in temperature
= (0.1kg + 0.2kg) x 390J/kg oC x (final equilibrium temperature - 17oC)
= 0.3kg x 390J/kg oC x (final equilibrium temperature - 17oC)

3. Set the heat lost equal to the heat gained and solve for the final equilibrium temperature:
2,925J = 0.3kg x 390J/kg oC x (final equilibrium temperature - 17oC)
Divide both sides by 0.3kg x 390J/kg oC:
(final equilibrium temperature - 17oC) = 2,925J / (0.3kg x 390J/kg oC)
(final equilibrium temperature - 17oC) = 26.5
Add 17oC to both sides:
final equilibrium temperature = 26.5 + 17
final equilibrium temperature = 43.5oC

Therefore, the final equilibrium temperature of the system is 43.5oC.