• Understand the relationship between Pressure, Volume and Temperature for ideal gases
• Record and plot PVT data using your Photon (template MATLAB script: PVT_diagrams.m)
• Complete this worksheet

• Breadboard
• Photon
• PASCO Ideal gas law syringe with thermistor and pressure transducer
• MPX 5700AP pressure sensor
• +5/-5 V power supply
• AD623 operational amplifier
• 10 kΩ resistors (x3)
• 4.7 kΩ resistor (or similar value)
• wires

In this experiment, you will use a syringe to take simultaneous measurements of the temperature and pressure of a gas (air) as it is compressed. The temperature is measured by a thermistor built into the base of the syringe whose response time is approximately half a second. The pressure is measured using a pressure transducer.

The Ideal Gas Law describes the equation of state for ideal gases; it relates the state variables of pressure, temperature and volume to one another. The Ideal gas equation can be written in terms of moles as:

Equation 1

where

It may also be written in terms of mass; by definition mass is the product of the number of moles (n) of a gas and the molecular mass (M) of the gas. Equation 2 shows the ideal gas law in terms of mass:

Equation 2

where

From the Ideal Gas Law, one can derive special cases for different processes.

Boyle’s Law states that the volume of a given amount of gas is inversely related to pressure when temperature is constant.

Equation 3

Charles’s Law states that the volume of a given amount of gas at constant pressure is directly proportional to its temperature.

Equation 4

Gay-Lussac’s Law states that for a given mass and constant volume of an ideal gas the pressure exerted on the sides of the container is directly proportional to its absolute temperature.

Equation 5

Avogadro’s Law states that the volume occupied by an ideal gas is directly proportional to the number of molecules of the gas in the container.

Equation 6

where n is equal to the number of molecules of gas (or the number of moles).

Combining Equations 3 – 6:

Equation 7

This is a good approximation for most gases under moderate pressure and temperature conditions.

Your kit contains a 60 mL syringe. The bottom of the syringe is instrumented with a thermistor (which is simply a resistor that changes resistance proportional to temperature) and a pressure sensor. You will be using a 0-700 kPa (0-101.5 psi) sensor shown in Figure 1.

Figure 1 MPX 5700AP Pressure Sensor

Construct a circuit using the MPX5700AP pressure sensor, following the analog output in Figure 1. Pin 3 of the sensor connects to the +5V from your power supply, and Pin 2 of the sensor connects to the GND on the Photon. Pin 1 is the output of the pressure sensor and connects to analog input A0 on the Photon.

As noted in the datasheet, this pressure sensor has the same transfer function as the one from Lab 1 Part 3 (see Equation 2). However, the pressure range for this sensor is 0-700 kPa (0-101.5 psi) and the accuracy is ±2.5%.

Construct the circuit in Figure 2. This circuit has 2 parts. Part 1 is wiring the amplifier using the AD623, which is the same op-amp we used in Lab 1 Part 2. Part 2 is using the thermistor embedded in the cap in a voltage divider on pin 2 of the amplifier and a reference voltage divider on pin 3.

A thermistor is simply a resistor whose resistance is dependent on temperature (more dependent than standard resistors). The thermistor we are using is PS-2125. The accuracy is ±0.5C and we can assume this accuracy for the range of temperatures we will be measuring. The relation between resistance and temperature is detailed in this datasheet, but this function is already provided for you in the MATLAB script.

Figure 2: Temperature Measurement Circuit

Connect the + and - output of the Power Supply to the + and – input pins 7 and 4 on the AD623. This is the power for the amplifier.

Rg is the gain resistor 4.7kΩ (yellow-pink-red). Connect it from pin 1 to 8.

Ground (GND) pin 5.

Pin 6 is the amplified output that connects to the analog input AI1 of the Photon.

Pins 2 and 3 are the signals to be compared and the difference amplified.

Construct 2 voltage dividers. The first divider will be the thermistor as R1 and a 10kΩ resistor as R2 (brown-black-orange). The junction of these two components connects to pin 2 of the AD623. The second divider acts as a reference. Connect the junction of these two resistors to pin 3 of the AD623.

Remember to connect the +5 and GND of both dividers as shown in Figure 2.

Figure 3: PVT Apparatus

At this point you should have the thermistor connected to the temperature measurement electronics and the pressure tube connected to the sensor, as shown in Figure 4.

Edit PVT_diagrams.m to record the increase in pressure and temperature with your Photon. If you need help with coding in MATLAB, refer to the MATLAB Tutorial.

Take at least 4 measurements over a range of volumes (we recommend 60, 50, 40, 30 mL). The uncertainty in the volume measurement is half of the smallest increment marking (±0.5 mL). This is the data you need to complete the worksheet.

If you need help with the uncertainty calculations, you can reference the error analysis section of the Technical Report Guidelines.

Set the initial volume in the syringe to 60mL. Push the plunger down to 50mL and wait a few seconds before recording the data using the matlab code. Without disconnecting the tube to the pressure sensor, from the 50mL mark press the plunger to 40mL and repeat for 40mL to 30mL.

Figure 4: PVT Circuit