Thermodynamics

Thermodynamics is the branch of physics that deals with heat and temperature and the conversion of heat into work and other forms of energy. Unlike kinetic theory, it describes systems through macroscopic variables such as pressure, volume, temperature and internal energy, without reference to molecules. The chapter begins with thermal equilibrium and the zeroth law of thermodynamics, which leads to the concept of temperature. It explains the internal energy of a system as the sum of the kinetic and potential energies of its molecules, and shows that heat and work are two ways of changing it. The first law of thermodynamics, dQ = dU + dW, is a statement of the conservation of energy. You will study specific heat capacity, state variables and the equation of state. You will also study quasi-static processes, including isothermal, adiabatic, isochoric, isobaric and cyclic processes, and calculate the work done in each, using the area under the P-V curve. Finally, the chapter introduces the second law of thermodynamics and distinguishes reversible from irreversible processes.

Detailed Worksheet: Thermodynamics Section A - Definitions (10 marks) 1. State the zeroth law of thermodynamics. (2 marks) 2. State the first law of thermodynamics and write its mathematical form. (2 marks) 3. Define an isothermal process and an adiabatic process. (2 marks) 4. Why is the work done in an isochoric process zero? (2 marks) 5. Give two examples of irreversible processes. (2 marks) Section B - Calculations and Applications (15 marks) 6. A system absorbs 500 J of heat and does 200 J of work. Find the change in its internal energy. (3 marks) 7. Find the work done when 1 mol of an ideal gas expands isothermally at 300 K to double its volume. Take R = 8.31 J/mol K and ln 2 = 0.693. (3 marks) 8. A gas at a constant pressure of 10^5 Pa expands by 0.002 m^3. Find the work done by the gas. (3 marks) 9. A monatomic ideal gas is compressed adiabatically to half its volume. By what factor does its pressure increase? Take 2^(5/3) = 3.17. (3 marks) 10. Find the heat needed to raise the temperature of 1 mol of a monatomic gas by 10 K at constant volume and at constant pressure. (3 marks) Section C - Diagrams (10 marks) 11. Draw P-V diagrams for isothermal and adiabatic expansions from the same initial state and explain which curve is steeper. (4 marks) 12. Draw a P-V diagram for a cyclic process and show that the work done equals the area enclosed. (3 marks) 13. Draw P-V diagrams for an isochoric and an isobaric process. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Derive the expression for the work done by an ideal gas in an isothermal expansion from volume V1 to V2. (5 marks) 15. Derive the expression for the work done in an adiabatic process and show that it is (P1V1 - P2V2)/(gamma - 1). (5 marks) 16. When 1 g of water at 100 degrees Celsius becomes steam at 1 atm, its volume changes from 1 cm^3 to 1671 cm^3. Find the work done and the change in internal energy. Take the latent heat as 2256 J/g and 1 atm = 1.013 x 10^5 Pa. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Take R = 8.31 J/mol K. Use the sign convention that heat given to the system and work done by the system are positive.