Lab 7: Study of Thermal Processes in Gases (PDF)

**Laboratory Work** **Title:** **Study of Thermal Processes in Gases: Measuring the Heat Capacity of a Gas at Constant Volume and Pressure** **Objective:** - To study thermal processes in gases using PhET Colorado simulation. - To measure and compare the heat capacity of a gas at constant v...

**Laboratory Work** **Title:** **Study of Thermal Processes in Gases: Measuring the Heat Capacity of a Gas at Constant Volume and Pressure** **Objective:** - To study thermal processes in gases using PhET Colorado simulation. - To measure and compare the heat capacity of a gas at constant volume (Cv) and constant pressure (Cp). - To verify the relationship Cp−Cv=R experimentally. **Equipment:** - Computer with internet access. - PhET Interactive Simulation: [[Gas Properties]](https://phet.colorado.edu/en/simulation/gas-properties). **Theory:** 1. **Heat Capacity**: - Cv: Heat capacity at constant volume is the amount of heat required to raise the temperature of a gas while keeping the volume constant. - Cp: Heat capacity at constant pressure is the amount of heat required to raise the temperature of a gas while keeping the pressure constant. 2. **Relation Between Cp and Cv**: - Cp−Cv=R, where RR is the universal gas constant (8.314 J/mol·K). 3. **Adiabatic Index (γ)**: - γ=Cp/Cv , which describes the relationship between the heat capacities. 4. **First Law of Thermodynamics**: - For constant volume, W=0W = 0, so ΔU=Q. - For constant pressure, Q=ΔU+WQ. **Procedure:** **Step 1: Accessing the Simulation** 1. Open the [[PhET Gas Properties simulation]](https://phet.colorado.edu/en/simulation/gas-properties). 2. Set the simulation to the **Ideal Gas Behavior** mode. **Step 2: Experiment for Constant Volume** 1. Select a gas (e.g., Neon). 2. Adjust the **Volume** to a fixed value using the slider. 3. Set the **Heater Power** to a low level (e.g., 5 units). 4. Record the initial temperature (T1T\_1). 5. Turn on the heater for a specific time interval (e.g., 30 seconds). 6. Record the final temperature (T2T\_2). 7. Calculate the heat added (QQ): Q=P×ΔtQ = P \\times \\Delta t **Step 3: Experiment for Constant Pressure** 1. Allow the gas to expand by adjusting the **Pressure** to a fixed value. 2. Repeat the heating process as above, recording T1T\_1 and T2T\_2. 3. Calculate Cp using the same formula: Cp=QnΔT **Step 4: Verification** 1. Verify the relationship Cp−Cv=R 2. Compute the adiabatic index γ=Cv/Cp **Observations:** **Experiment** **Heat Added (Q)** **Initial Temp (T1)** **Final Temp (T2)** **ΔT** **Cv or Cp** ------------------- -------------------- ----------------------- --------------------- -------- -------------- Constant Volume Constant Pressure **Theoretical Questions:** 1. Define heat capacity. What is the difference between specific heat capacity and molar heat capacity? 2. Explain Cv and Cp. Why is Cp\>Cv? 3. State the first law of thermodynamics and describe how it applies to isochoric and isobaric processes. 4. Derive the relationship Cp−Cv=R for an ideal gas. 5. What is an adiabatic process? How does it differ from an isochoric process? 6. What assumptions are made in the ideal gas law? How do they affect the accuracy of heat capacity measurements? 7. Define the adiabatic index γ. Why is it important? 8. Describe how degrees of freedom in a gas affect its heat capacities. 9. How is heat capacity related to the internal energy of an ideal gas? **Problems:** **Problem 1:** A 1.5 mole sample of an ideal gas undergoes an isochoric process where 500 J of heat is supplied, increasing its temperature by 10 K. Determine Cv. **Problem 2:** A monoatomic gas is heated at constant pressure, increasing its temperature from 300 K to 400 K. If the gas absorbs 2,000 J of heat, calculate the number of moles of gas and Cp. **Problem 3:** Derive the work done when a gas expands isobarically from an initial volume of 1.0 m3 to 1.5 m3 at a constant pressure of 100,000 Pa. Relate this to Cp. **Problem 4:** An ideal gas is compressed adiabatically. If the initial pressure and temperature are 2 atm and 300 K, respectively, and the final pressure is 4 atm, calculate the final temperature. Assume the gas is diatomic (γ=1.4). **Problem 5:** Using the PhET simulation, measure the heat added to a gas at constant volume and at constant pressure. If R=8.314 J/mol, verify Cp−Cv=R