Calorimetry: Calculate the specific heat capacity of aluminum.

Calorimetry is the branch of thermodynamics that deals with the measurement of the quantity of heat exchanged during a physical or chemical process. In order to solve calorimetry problems, you need to follow the following steps:


Step 1: Identify the problem

The first step in solving any calorimetry problem is to identify what is being asked for. Read the problem carefully and determine what needs to be found.


Step 2: Determine the type of calorimetry problem

There are two types of calorimetry problems: constant pressure calorimetry problems and constant volume calorimetry problems. You need to determine the type of problem you are working on.


Step 3: Draw a diagram

Drawing a diagram of the problem can help you visualize the situation and organize your thoughts. It can also help you to keep track of what information you have and what information you need.


Step 4: Determine the heat transfer equation

The heat transfer equation for constant pressure calorimetry problems is Q = mCpΔT, where Q is the heat transferred, m is the mass of the substance, Cp is the specific heat capacity of the substance, and ΔT is the change in temperature. The heat transfer equation for constant volume calorimetry problems is Q = mCvΔT, where Cv is the specific heat capacity at constant volume.


Step 5: Calculate the heat transfer

Using the appropriate heat transfer equation from Step 4, calculate the amount of heat transferred.


Step 6: Check the units

Make sure that all the units are consistent with the units in the heat transfer equation. If the units are not consistent, convert them to the appropriate units.


Step 7: Check the signs

Make sure to use the correct sign for the heat transfer. If heat is being added to the system, the sign should be positive. If heat is being removed from the system, the sign should be negative.


Step 8: Solve the problem

Now that you have all the necessary information, you can solve the problem using the appropriate equation.


Step 9: Check the answer

Double-check your calculations and make sure that your answer makes sense in the context of the problem.


Example problem:


A 100 g sample of water is heated from 20°C to 70°C. Calculate the amount of heat transferred.


Step 1: Identify the problem

We are being asked to find the amount of heat transferred.


Step 2: Determine the type of calorimetry problem

This is a constant pressure calorimetry problem.


Step 3: Draw a diagram

No diagram is necessary for this problem.


Step 4: Determine the heat transfer equation

The heat transfer equation for constant pressure calorimetry problems is Q = mCpΔT.


Step 5: Calculate the heat transfer

Q = (0.1 kg)(4.18 J/g°C)(70°C - 20°C) = 167.2 J


Step 6: Check the units

The units in the equation are consistent. 


Step 7: Check the signs

Heat is being added to the system, so the sign should be positive.


Step 8: Solve the problem

Q = 167.2 J


Step 9: Check the answer

The answer is reasonable, as it represents a significant amount of heat being added to the water to increase its temperature by 50°C.




A 50 g piece of aluminum at 80°C is placed in 100 g of water at 20°C. The final temperature of the mixture is 25°C. Calculate the specific heat capacity of aluminum.


Step 1: Identify the problem

We are being asked to find the specific heat capacity of aluminum.


Step 2: Determine the type of calorimetry problem

This is a constant pressure calorimetry problem.


Step 3: Draw a diagram

We can draw a simple diagram of the setup:


        | 50 g aluminum @ 80°C |

        |                                           |

        ---[ 100 g water @ 20°C ]---

        |                                          |

        |                                          |

        |                                          |

        |---------------------------|

               Mixture @ 25°C


Step 4: Determine the heat transfer equation

The heat transfer equation for constant pressure calorimetry problems is Q = mCpΔT, where Q is the heat transferred, m is the mass of the substance, Cp is the specific heat capacity of the substance, and ΔT is the change in temperature.


We can use this equation to calculate the heat transferred from the aluminum to the water, and then from that we can calculate the specific heat capacity of aluminum.


Step 5: Calculate the heat transfer

First, we need to calculate the heat transferred from the aluminum to the water. We can do this using the following equation:


Q_aluminum = m_aluminum * Cp_aluminum * ΔT_aluminum


where m_aluminum is the mass of the aluminum, Cp_aluminum is the specific heat capacity of aluminum, and ΔT_aluminum is the change in temperature of the aluminum.


Q_aluminum = (0.05 kg) * Cp_aluminum * (80°C - 25°C)

Q_aluminum = 1.77 * Cp_aluminum


Next, we need to calculate the heat transferred from the water to the aluminum. We can use the following equation:


Q_water = m_water * Cp_water * ΔT_water


where m_water is the mass of the water, Cp_water is the specific heat capacity of water, and ΔT_water is the change in temperature of the water.


Q_water = (0.1 kg) * (4.18 J/g°C) * (25°C - 20°C)

Q_water = 20.9 J


Since heat is conserved, we know that the heat transferred from the aluminum to the water must be equal to the heat transferred from the water to the aluminum:


Q_aluminum = Q_water

1.77 * Cp_aluminum = 20.9

Cp_aluminum = 11.8 J/g°C


Step 6: Check the units

The units in the equation are consistent.


Step 7: Check the signs

Heat is being transferred from the aluminum to the water, so the sign should be negative for Q_aluminum.


Step 8: Solve the problem

Cp_aluminum = 11.8 J/g°C


Step 9: Check the answer

The answer is reasonable, as the specific heat capacity of aluminum is generally around 0.9 J/g°C, so the calculated value of 11.8 J/g°C is much larger and suggests that the aluminum used in this problem may not be pure aluminum.

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