Work andHeat Mechanical Energy E mech = K + U If there are only conservative forces ( ex. Gravity force, spring force) in the system ΔE mech = ΔK + ΔU = 0 If there is friction forces ΔE mech = ΔK + ΔU = W fric < 0 General case ΔE mech + ΔE th = W ext ΔE th is the change of thermal energy and W ext is the work done by the external force. The systems we want to study in thermodynamics are stationary containers gases or liquids, whose center-of –mass mechanical energy does not change. Thus ΔE mech = 0

Thermal Energy Thermal energy E th is associated with the system’s temperature. We now need to be a bit more specific During a phase change, from solid to liquid or from liquid to gas, a system’s thermal energy increases but its temperature does not. If there are no phase changes, increasing the system’s temperature increase its thermal energy. A system’s thermal energy does not change (ΔE th = 0) during an isothermal process (ΔT =0)

Work Work is the energy transferred between a system and environment when a net force acts on the system over a distance. The sign of the work Work is positive when the force is in the direction of motion Work is negative when the force is opposite to the motion

Heat The energy transferred in a thermal interaction is called heat The symbol for heat is Q The energy equation now becomes ΔE sys = ΔE mech + ΔE th = W ext + Q Quick quiz: A gas cylinder and piston are covered with heavy insulation. The piston is pushed into the cylinder, compressing the gas. In the process. The gas temperature Increases Decreases Doesn’t change

Work in Ideal-Gas Processes The work done on the system When we press the gas, the gas volume becomes smaller, so the total work done by the environment on the gas

Work in some special processes Isochoric Process W = 0 Isobaric Process W = -PΔV Isothermal Process Work depends on path

Finding work from the P-V diagram W = the negative of the area under the PV curve between Vi and Vf W < 0 W > 0

Heat and Thermal interactions Heat is the energy transferred during a thermal interaction Units of heat The SI unit of heat is joule. Historically, unit for measuring heat, is calorie A cal = the quantity of heat needed to change the temperature of 1 g of water by 1 o C. 1cal = J 1 food calorie = 1 Cal = 1000 cal =1 kcal

Distinguish between heat, temperature, and thermal energy Thermal energy is an energy of the system due to the motion of its atoms and molecules. Thermal energy is a state variable, it may change during a process. The system’s thermal energy continues to exist even if the system is isolated and not interacting thermally with its environment Heat is energy transferred between the system and the environment as they interact. Heat is not a particular form of energy, nor is it a state variable. Heat may cause the system’s thermal energy to change, but that does not mean that heat and thermal energy are the same thing. Temperature is a state variable, it is related to the thermal energy per molecule. But not the same thing.

Specific Heat What happens to a system when you change its thermal energy? The temperature of the system changes The system undergoes a phase change, such as melting or freezing Specific Heat C : The amount of energy that raises the temperature of 1 Kg of A substance by 1 K ( or 1C) is called specific heat. In other words, the thermal energy of the system changes by ΔE th = Mc ΔT ( Kelvin and Celsius temperature scales have the same step size. ) The first law of thermodynamics ΔE th = W + Q, In working with solids And liquids, we almost always change the temperature by heating, so W = 0, Then the heat needed to bring about a temperature change ΔT is Q = Mc ΔT. Molar specific heat: The amount of energy that raises the temperature of 1 mol of a substance by 1K. It depends on the molar mass. Table 17.2 (page 527) list few specific heat and molar specific heats of solids and Liquids.

Phase change and heat of transformation A phase change is characterized by a change in thermal energy without change in temperature Heat of fusion L f : the heat of transformation for 1 Kg substance between a solid and liquid. Heat of vaporization L v the heat of transformation for 1 Kg substance between a liquid and gas. Q = ± M L f melt/freeze Q = ± M L v boil/condense Table 17.3 list few melting/boiling temperatures and heat of transformation. For systems that undergo a temperature change, Q = Mc (T f – T i ). For systems that undergo a phase change Q = ± ML, Supply the correct sign by observing whether energy enters or leaves the system during the transition.

The specific heats of gases The heat required to cause a specified temperature change depends on the process by which the gas changes Process A and B, which start on the Ti And end on the Tf, have the same temperature Change ÄT = Tf-Ti, But different amount of Heat is required. ÄT at constant volume ÄT at constant pressure C v is the molar specific heat at constant Volume. C p is the molar specific heat at constant pressure

C p and C v ΔE th (constant volume process) = W + Q = 0 + nC v ΔT = nC v ΔT ΔE th (constant pressure process) = W + Q = -pΔV + nC p ΔT If both have the same ΔT, ΔE th in tow process is the same -pΔV + nC p ΔT = nC v ΔT Using the ideal gas law, in constant-pressure process pΔV = nR ΔT -nR ΔT + nC p ΔT = nC v ΔT C p = C v + R ΔE th = nC v ΔT (any idea-gas process)