A 45.0g sample of polyisoprene, which has a specific heat capacity of 1.880·J·g−1°C−1, is dropped into an insulated container containing 100.0g of water at 20.0°C and a constant pressure of 1atm. The initial temperature of the polyisoprene is 84.4°C.Assuming no heat is absorbed from or by the container, or the surroundings, calculate the equilibrium temperature of the water. Be sure your answer has the correct number of significant digits.
Question
A 45.0g sample of polyisoprene, which has a specific heat capacity of 1.880·J·g−1°C−1, is dropped into an insulated container containing 100.0g of water at 20.0°C and a constant pressure of 1atm. The initial temperature of the polyisoprene is 84.4°C.Assuming no heat is absorbed from or by the container, or the surroundings, calculate the equilibrium temperature of the water. Be sure your answer has the correct number of significant digits.
Solution
To solve this problem, we need to use the principle of conservation of energy, which states that the heat lost by the polyisoprene will be equal to the heat gained by the water.
The formula for heat transfer is Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, we calculate the heat lost by the polyisoprene:
Q_polyisoprene = m_polyisoprene * c_polyisoprene * (T_initial_polyisoprene - T_final)
We don't know the final temperature yet, so we'll leave it as T_final.
Q_polyisoprene = 45.0g * 1.880 J/g°C * (84.4°C - T_final)
Next, we calculate the heat gained by the water. The specific heat capacity of water is 4.184 J/g°C.
Q_water = m_water * c_water * (T_final - T_initial_water)
Q_water = 100.0g * 4.184 J/g°C * (T_final - 20.0°C)
Since the heat lost by the polyisoprene is equal to the heat gained by the water, we can set the two equations equal to each other and solve for T_final:
45.0g * 1.880 J/g°C * (84.4°C - T_final) = 100.0g * 4.184 J/g°C * (T_final - 20.0°C)
Solving this equation gives T_final = 26.8°C. Therefore, the equilibrium temperature of the water is 26.8°C.
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