The First Law of Thermodynamics

1. The First Law of Thermodynamics Signs for heat (q) and work (w) Thermodynamic transformations q is + if heat is added to system q is – if heat is lost by system w is + if work is done on the system. w is – if work is done by the system.

3. System and Surroundings Adiabatic - The orange walls insulate the system completely (no heat can pass through) Isochoric - Literally means no work. For our purposes it means the Volume is constant. Isothermal - The thermal reservoir keeps the system at a constant temperature Free Expansion - The piston offers no resistance (there is vacuum above the brown piston) Isobaric - The force on the piston from above is constant (for example atmospheric pressure) Thermal reservoir

4. Different paths in the Expansion of a gas Consider the expansion of an ideal gas with various coupling between it (the system) and the surroundings • Free expansion (No external Pressure) • Isothermal (Constant Temperature) • Adiabatic (No heat transfer) • Isobaric (Constant pressure) • Isochoric (No work) Each of these represents different coupling Between the system and the surroundings. Thermal reservoir

5. Different paths in the Expansion of a gas Consider the expansion of an ideal gas with various coupling between it (the system) and the surroundings • Free expansion (No external Pressure) • Isothermal (Constant Temperature) • Adiabatic (No heat transfer) • Isobaric (Constant pressure) • Isochoric (No work) What is the work in a free expansion? For an Ideal gas what is \Delta U for an Isothermal Expansion? dU = ? For an Adiabatic process? dU = ? For an Isochoric process? Thermal reservoir

6. Free Expansion the same final state the same initial state Internal energy of an ideal gas Partition is broken and gas is Allowed to expand in an adiabatic (no heat transfer container) Controlled expansion (Isothermal Reversible) Work done No work done Different paths Heat exchanged No heat exchanged Is DU is the same for both processes?

7. Problem Imagine that an ideal monatomic gas is taken from its initial state A to state B by an isothermal process, from B to C by an isobaric process, and from C back to its initial state A by an isochoric process. Fill in the signs of Q, W, and ¢U for each step. P, A 2 0 T=const B 1 C 1 2 V

8. Problem Imagine that an ideal monatomic gas is taken from its initial state A to state B by an isothermal process, from B to C by an isobaric process, and from C back to its initial state A by an isochoric process. Fill in the signs of Q, W, and ¢U for each step. P A 2 + -- 0 T=const -- + -- B 1 C + 0 + 1 2 V Is this an engine?

9. Grains of sand In limit of infinitesmal changes, system moves through equilibrium states during transition-->reversible process Reversible Process Remove one grain of sand at a time. Allow system to equilibrate Pressure decreases by very small amount Volume increases by very small amount. A reversible process is one where every step of the path is at equilibrium with its surroundings

10. Examples of Reversible and Irreversible • Jumping into a pool? (from the perspective of the water) • Getting into a pool slowly? • Free expansion of a gas • Isothermal expansion (piston must move very slowly for bath) • Moving a glass slowly

11. Isothermal Reversible Process: T constant: Ideal gas For an ideal gas U= q + w =0 -w = q

12. Isothermal Reversible Process: T constant: Ideal gas For an ideal gas E=q+w=0 w=-q In rev process Pext=Pgas=P=nRT/V w=-P1V -P2V- …