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 250.0g of water at 85.0°C and a constant pressure of 1atm. The initial temperature of the polyisoprene is 8.0°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 250.0g of water at 85.0°C and a constant pressure of 1atm. The initial temperature of the polyisoprene is 8.0°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 1
To solve this problem, we need to use the principle of conservation of energy, which states that the heat lost by the hot substance (water) is equal to the heat gained by the cold substance (polyisoprene).
The formula for heat transfer is Q = mcΔT, where:
- Q is the heat transferred,
- m is the mass of the substance,
- c is the specific heat capacity of the substance, and
- ΔT is the change in temperature of the substance.
First, let's calculate the heat lost by the water:
Q_water = m_water * c_water * ΔT_water
where:
- m_water = 250.0 g,
- c_water = 4.184 J/g°C (specific heat capacity of water), and
- ΔT_water = T_final - T_initial = T_final - 85.0°C.
Next, let's calculate the heat gained by the polyisoprene:
Q_polyisoprene = m_polyisoprene * c_polyisoprene * ΔT_polyisoprene
where:
- m_polyisoprene = 45.0 g,
- c_polyisoprene = 1.880 J/g°C, and
- ΔT_polyisoprene = T_final - T_initial = T_final - 8.0°C.
Since the heat lost by the water is equal to the heat gained by the polyisoprene, we can set the two equations equal to each other and solve for T_final:
250.0 g * 4.184 J/g°C * (T_final - 85.0°C) = 45.0 g * 1.880 J/g°C * (T_final - 8.0°C)
Solving this equation for T_final will give us the equilibrium temperature of the water.
Solution 2
To solve this problem, we need to use the principle of conservation of energy, which states that the heat lost by the hot substance (water) is equal to the heat gained by the cold substance (polyisoprene).
The formula for heat transfer is Q = mcΔT, where:
- Q is the heat transferred,
- m is the mass of the substance,
- c is the specific heat capacity of the substance, and
- ΔT is the change in temperature of the substance.
First, let's calculate the heat lost by the water: Q_water = m_water * c_water * (T_initial_water - T_final), where:
- m_water = 250.0 g,
- c_water = 4.184 J/g°C (specific heat capacity of water), and
- T_initial_water = 85.0°C.
Next, let's calculate the heat gained by the polyisoprene: Q_polyisoprene = m_polyisoprene * c_polyisoprene * (T_final - T_initial_polyisoprene), where:
- m_polyisoprene = 45.0 g,
- c_polyisoprene = 1.880 J/g°C, and
- T_initial_polyisoprene = 8.0°C.
Since the heat lost by the water is equal to the heat gained by the polyisoprene, we can set the two equations equal to each other and solve for T_final:
250.0 g * 4.184 J/g°C * (85.0°C - T_final) = 45.0 g * 1.880 J/g°C * (T_final - 8.0°C).
Solving this equation will give us the equilibrium temperature of the water.
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