Question

1. Name three characteristics of the atoms in a gas that are essential for the gas to be ideal. Explain why these three qualities of the atoms or molecules make the gas ideal.

2. Considering the Boltzmann distribution of atomic/molecular speeds for an ideal gas at temperature T (in K) , order the following speeds from smallest to largest: average speed, most probable speed, and root mean squared speed. Why are they different speeds?

3. What is the most important speed in Conceptual Question 2? Why?

4. Which molar specific heat is largest C_p or C_v? Why?

5. Which is larger Cp for a diatomic gas like hydrogen (H₂) when compared to a polyatomic gas like Ether { (C₂H₅)₂ O } ? Why is there a difference?

Problems:

1. Three moles of an ideal gas at 135C and 0.5 atm is allowed to expand to 1.0 atm at constant pressure to a volume twice as large. What is the new temperature?

2. An ideal gas is confined to a constant volume container and heated from a pressure of 1 atm at room temperature to a pressure of 5 atm. What is the final temperature?

3. A balloon is to be inflated to a volume of 5 m³ with Helium at atmospheric pressure and temperature 35C. What would be the smallest volume of a tank, in liters, that could store the Helium at room temperature (22 C) and 50 atm pressure?

4. A monatomic ideal gas is initially at a pressure of 1.00 atm in a 1.00 L cylindrical container with a piston on one side. It is compressed to a volume of 0.250 L.

a) graph the process on a PV diagram assuming it is i) adiabatic and ii) isothermal.

b) Determine the final pressure if the process is i) adiabatic or ii) isothermal.

5. A gas mixture contains 3.0 moles of O₂ and 9.0 moles of Argon (Ar) at a temperature of 300.0 K. What is the total thermal internal energy of the gas mixture considering both gases. (Ignore vibrational energy)

6. A gas is at constant pressure of 2.4 x 10⁵ N/m². Its volume increases by

1.2 x 10^-2 m³ as 3200 J of heat energy s transfer to the gas. Find the change in thermal energy of the gas.

7. (EC) Derive the equation for the pressure and volume changes during an adiabatic process- pVγ = constant, where Υ= C_p/C_{v .}

8. An ideal gas expands such that no heat is exchanged with the surroundings. It then undergoes a process for which no work is done to return to the original pressure. Finally, it undergoes a constant pressure process to return to the original state of the gas.

a) What thermodynamic process is occurring in each of the steps. Explain your reasoning.

b) Sketch the cycle on a PV diagram.

c) What represents the net work done by the process each cycle?

d) Is heat rejected during the process? If so, what represents the amount of heat rejected per cycle?

9. Derive the equation for the work done by an ideal gas during an isothermal expansion from volume one to volume two.

10. The PV diagram shown below shows a set of thermodynamic processes that make up a cycle ABCDA for a monatomic ideal gas. AB is an isothermal expansion occurring at 375 K. There are 2.00 moles of gas undergoing the cycle with

P_A = 1.01 x 10⁵ Pa, P_B = 5.05 x 10⁵ Pa, and P_C = 2.02 x 10⁵ Pa.

a) find the volumes V_A and V_B

b) find the work done in each process and the total net work done for one cycle

c) find the change in thermal energy during the constant volume process BC

Answer 1