Question

Design an Experiment Describe a procedure you could follow to determine the specific heat of a 45-g piece of metal.

Short answer

To determine the specific heat of a 45-g piece of metal, set up a simple calorimeter using a Styrofoam cup filled with 150 mL of water and a thermometer. Heat the metal in a water bath on a hot plate to around 90-100°C. Transfer the heated metal to the calorimeter, observing the change in temperature in the cup. Calculate the specific heat using the formula: \(c_{metal} = \frac{m_{water}c_{water}(T3 - T1)}{m_{metal}(T2-T3)}\), taking into account the mass and temperature values obtained during the experiment.

Step-by-step solution

Assemble the materials

Collect the following materials for the experiment: 1. 45-g piece of metal 2. Styrofoam cup 3. Thermometer 4. Hot plate or heat source 5. Beaker 6. Water 7. String 8. Balance

Prepare the calorimeter

Fill the Styrofoam cup with approximately 150 mL of water. Measure and note down the initial temperature of the water (T1). Place the thermometer in the water to monitor the temperature.

Weigh the metal

Use the balance to confirm the mass of the metal piece. It should be 45 grams. If it's slightly off, note down the actual mass.

Heat the metal

Place the piece of metal in a beaker with water on the hot plate. Heat the water until it reaches a temperature of around 90 to 100°C. Carefully monitor the temperature using a thermometer, and once it reaches the desired temperature, note down the temperature as the initial temperature of the metal (T2).

Transfer the metal to the calorimeter

Using a string or tongs, carefully remove the heated metal piece from the beaker and quickly transfer it to the Styrofoam cup with water. Make sure to minimize the heat loss during the transfer.

Observe the temperature change

As the metal transfers its heat energy to the water, the temperature in the cup will rise. Record the highest temperature the water reaches (T3) before it starts cooling down.

Calculate the specific heat of the metal

Using the temperature data, we can now calculate the specific heat capacity of the metal. We know that the heat energy gained by the water (Q_water) should be equal to the heat energy lost by the metal (Q_metal). So, we have: \[Q_{metal} = Q_{water}\] \[mc(T2 - T3) = mc(T3 - T1)\] Rearrange the equation to solve for the specific heat of the metal (c_metal): \[c_{metal} = \frac{m_{water}c_{water}(T3 - T1)}{m_{metal}(T2-T3)}\] Substitute the values for mass, temperatures, and the specific heat of water (4.18 J/g°C) into the equation and solve for the specific heat of the metal: \[c_{metal} = \frac{(150\,g)(4.18\,J/g°C)(T3 - T1)}{(45\,g)(T2-T3)}\] Once you have calculated the specific heat of the metal, you can compare it with the known specific heat values of different metals to potentially determine the type of metal of the 45-g piece.

Key concepts

Calorimetry

Calorimetry is an essential experiment in the field of thermodynamics, focused on measuring the heat of chemical reactions or physical changes. The process involves the use of a calorimeter, which is a device designed to insulate the reaction or substance from the external environment, thereby minimizing energy exchange.

In the experiment to determine the specific heat of a metal, a simple calorimeter can be constructed using a Styrofoam cup, which serves to insulate the system. By observing the temperature change of water, into which a heated metal piece is placed, we can deduce the amount of heat transferred during the process. The act of measuring the heat exchange between the metal and water, paired with the known value of water's specific heat, allows us to solve for the metal's specific heat through careful calculations.

Thermal Energy Transfer

Thermal energy transfer is a key concept in studying heat movement from one object to another. In our specific heat experiment, the metal, once heated, holds thermal energy that will naturally flow to the cooler water when they come into contact. This is known as heat transfer.

There are three primary methods of heat transfer: conduction, convection, and radiation. Our specific heat experiment primarily involves conduction, where heat energy is transferred through direct contact. When the metal's thermal energy is passed to the water, the energy absorbed causes the water's temperature to rise. Monitoring this temperature change is crucial as it directly correlates with the amount of heat energy transferred.

Scientific Method

The scientific method is the backbone of conducting experiments and involves systematic observation, measurement, experiment, formulating, testing, and modifying hypotheses. In the process of determining the specific heat of a metal, the scientific method plays an integral role.

Firstly, a hypothesis would be that the metal's specific heat can be determined through thermal energy transfer to water. We then operationalize this through a step-by-step experiment involving the preparation and use of a simple calorimeter. Observations and measurements are meticulously noted, namely the masses of the substances and the temperature changes involved. Once the data is collected, we can apply formulas to test our hypothesis and draw conclusions based on the calculated specific heat.

Measuring Temperature Change

Measuring temperature change is a fundamental aspect of calorimetry. The magnitude of temperature change in a substance, when heat is added or removed, helps determine the specific heat capacity of the substance.

In our experiment, it's crucial to precisely measure the initial temperature of the water in the calorimeter, the temperature of the heated metal just before it's transferred to the calorimeter, and finally, the highest temperature the water reaches after the metal is immersed. These temperature readings \(T1, T2, and T3\) are then used in the specific heat formula to calculate the unknown specific heat value of the metal.