Question

Design an experiment complete with instrumentation to determine the specific heats of a gas using a resistance heater. Discuss how the experiment will be conducted, what measurements need to be taken, and how the specific heats will be determined. What are the sources of error in your system? How can you minimize the experimental error?

Short answer

Question: Design an experiment to measure the specific heat of a gas at constant volume and at constant pressure. Discuss possible sources of error and how to minimize these errors in the experiment. Answer: To measure the specific heat of a gas at constant volume (Cv), we would use a closed container with a known mass of gas, a resistance heater, thermometer, pressure sensor, and a data acquisition system. The volume of the container would be kept constant and the gas would be heated until it reaches a new equilibrium. The initial and final temperature and pressure would be recorded to calculate the heat supplied by the heater and subsequently determine Cv by the formula: Cv = (Q) / (mass × (T2 - T1)). For the specific heat of a gas at constant pressure (Cp), the same setup would be maintained albeit the experiment maintained under constant pressure. Initial and final temperature and volume readings would be used to determine Cp using the formula: Cp = (Q) / (mass × (T2 - T1)). Possible errors include heat loss to surroundings, inaccurate temperature and pressure readings, non-uniform temperature distribution in the gas, and gas leaks. These can be minimized by insulating the container, using accurate and calibrated measurement devices, ensuring uniform temperature distribution via stirring or using a fan, and ensuring proper sealing to prevent gas leaks.

Step-by-step solution

1. Understanding specific heat concept

Specific heat is defined as the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius (or Kelvin). For a gas, there are two specific heats: specific heat at constant pressure (Cp) and specific heat at constant volume (Cv). The distinction exists because gases can do work when heated, resulting in a difference in heat input at constant pressure or constant volume.

2. Design the experimental set-up

The experimental set-up should include a closed container filled with the known mass of the gas under investigation, a resistance heater, a thermometer, a pressure sensor, and a data acquisition system. The resistance heater will supply the required heat energy to increase the gas temperature while the thermometer and pressure sensor will measure the corresponding temperature and pressure changes.

3. Measuring specific heat at constant volume (Cv)

First, we need to measure the specific heat at constant volume. The following steps must be followed: a) Maintain the volume of the container constant by using a suitable apparatus b) Start the resistance heater and begin heating the gas c) Record the initial temperature (T1) and initial pressure (P1) of the gas d) Allow the gas to reach a new equilibrium, and record the final temperature (T2) and final pressure (P2) e) Calculate the heat supplied by the resistance heater (Q) f) Determine the specific heat at constant volume, Cv, using the formula: Cv = (Q) / (mass × (T2 - T1))

4. Measuring specific heat at constant pressure (Cp)

Next, we need to measure the specific heat at constant pressure. The following steps must be followed: a) Maintain the pressure of the container constant by using a suitable apparatus b) Start the resistance heater and begin heating the gas c) Record the initial temperature (T1) and initial volume (V1) of the gas d) Allow the gas to reach a new equilibrium, and record the final temperature (T2) and final volume (V2) e) Calculate the heat supplied by the resistance heater (Q) f) Determine the specific heat at constant pressure, Cp, using the formula: Cp = (Q) / (mass × (T2 - T1))

5. Sources of error in the experiment

Possible sources of error in the experiment include: a) Heat losses to the surroundings, which can affect the amount of heat supplied to the gas b) Inaccurate temperature and pressure measurements due to instrument limitations c) Non-uniform temperature distribution in the gas d) Gas leaks during the experiment

6. Minimizing experimental error

To minimize the experimental error, the following precautions should be taken: a) Insulate the container to minimize heat losses to the surroundings b) Use accurate and calibrated thermometers and pressure sensors for precise measurements c) Ensure a uniform temperature distribution by stirring the gas or using a fan during the experiment d) Ensure proper sealing of all joints and connections in the experimental setup to prevent gas leaks.