The First Law of Thermodynamics

Thermodynamics Very general: describes “working substances” in terms of pressure, volume, temperature, ... A thermodynamic system interacts with its surroundings by exchange of heat, by doing work, or both A (macro)state describes the system, a process makes the system go from one state to another

State variables state variable: precisely measurable physical property which characterizes the (macro)state of a system, independent of how the system was brought to that state Examples: p, N, V, T, U Any property that is a combination of state variables is a state variable itself

Definitions If the pressure is constant during a process, it is said to be isobaric V constant: isochoric T constant: isothermal no heat transfer: adiabatic/isentropic

p,V and p,T diagrams It is often useful to plot p against V or p against T in a graph. Which processes are isothermal, isobaric, isochoric? 1 p p 4 2 5 3 6 V T

Changing internal energy How can this be achieved? by making the system do work W by heating the system Q Note signs: W>0: work done by system Q>0: heat flows into system W Q reservoir

Work Mechanics: if gas expands in the direction of force F over distance dx the work done is Fdx. Write as function of pressure: F=pA, dV=Adx so W = pdV Integral form: W =  pdV dV A F dx

Work for different processes Isochoric: V2 = V1 so W = 0 Isobaric: p is constant so Isothermal: p varies so we must write

Process variables Heat and work are variables associated with a process. They are not state variables! 1 1 p p W 2 2 W V V

The first law of thermodynamics Q = U + W Warning! U: ideal gas: kinetic energy only real gas: small contribution from potential energy Warning! W: work done by gas expanding against pressure mechanical work e.g. to lift piston

Internal energy is a state variable Experiments have shown: Although neither Q nor W are state variables, the internal energy is a state variable In this sense the First Law of Thermodynamics contains more than just conservation of energy

Question An ideal gas expands by 20% of its original volume. The work done does not depend on a) the mass of the piston b) what gas is in this piston c) the pressure inside the piston d) the pressure outside the piston

Question When ice melts at atmospheric pressure, its volume decreases. The change in internal energy is a) greater than the heat added b) equal to the heat added c) less than the heat added d) we can’t tell

Question When water boils at atmospheric pressure, its temperature remains 100 °C. This implies that a) The kinetic energy of the molecules doesn’t change b) Most of the heat added is used to expand c) The internal energy doesn’t change d) No heat needs to be added to the system

PS225 – Thermal Physics topics The atomic hypothesis Heat and heat transfer Kinetic theory The Boltzmann factor The First Law of Thermodynamics Specific Heat Entropy Heat engines Phase transitions