First Law of Thermodynamics Physics 313 Professor Lee Carkner Lecture 8

Exercise #6 Spring  Work done on spring  W =  F dx =  kx dx = ½kx 2 = ½k(x 2 2 –x 1 2 )  If the spring is initially unstretched, x 1 = 0   Spring and gas work  displacement of spring  V = A  X  = 0.25  x,  x = 0.1 m, x 2 = 0.1 m  W = ½kx 2 2 = (½)(150)(0.1) 2 =   P = W/  V = 0.75/0.025 = 30 kPa   PV = nRT  T = PV/nR = (30000)(0.025)/(1)(8.31) =

Heat  What is heat?   Heat is not a state variable   No heat transfer if:    Heat is energy and can occur with different processes 

Isochoric Heat   If heat is added the temperature of the system will rise   Any heat exchange directly affects the internal energy 

Adiabatic Work  In an adiabatic system no heat can flow   For any adiabatic process by which the system move from state 1 to state 2 the total amount of work is a constant   This is not normally true   This work changes the internal energy

Internal Energy  When heat flows into the system or work is done on a system the system gains energy   The internal energy is a property of a system and can be expressed in terms of thermodynamic coordinates   We will often discuss a change in internal energy (  U or dU)

First Law of Thermodynamics  Energy is conserved   Can write in differential form as  dU is a change in internal energy   dQ and dW are small amounts of heat or work 

Notes on the First Law  Heat is defined thermodynamically by the first law:  Can also write for work:  Sign Convention  Heat into a system is positive   Work done on the system is positive   This convention can be changed but the first law then also must be changed

Notes on Heat  Heat was once thought to be a fluid within a body   People began to suspect that heat was a form of energy in the early 1800’s, but couldn’t prove it   Joule demonstrated the equivalence of heat and work in the 1840’s 

Special Cases  Adiabatic:   U = W   Isochoric:   U = Q 

Heat and Internal Energy  If a Styrofoam block and a steel block are both heated the same amount which is hotter?  Why?  Q = C  T 

Specific Heat   We will also use the heat capacity per mole:  Where n is number of moles or (m/M) total mass divided by molar mass

Heat Capacities  We can express the heat capacity in terms of differential changes in temperature and heat C = dQ/dT  We can then define two specific quantities:  C V = (dQ/dT) V  C P = (dQ/dT) P  Note that C is a function of temperature 

Internal Energy  We can write the heat flow into a system as:  For an isochoric system   So:   The change in internal energy is a function of the change in temperature

Heat Conservation   All objects within the boundary will exchange heat until they are in thermodynamic equilibrium (equal T)   Lost to surroundings

Calorimetry   A calorimeter must :  produce a well defined amount of heat   Monitor temperature   Heat produced must all go into raising temperature of sample 