Thermodynamics
25 September 2017 15:25
• Thermodynamics is concerned with the study of Work Heat
transformations in energy and the transformation Energy is the capacity to do work • Energy is transferred as heat - the energy of a
of heat into work. It tells us: Work is the motion against an opposing force system changes due to a temperature difference
○ Whether chemical reactions/processes will • Work = force x distance (force = mass x acceleration) between the system and the surroundings.
occur spontaneously or not • The work done is positive (w>0) if energy is • Enthalpy (H) is the "heat content" of a compound
○ Why reactions reach equilibrium, what the transferred into the system. • Often study the change in energy of compounds
composition is at equilibrium, and the There are two contributions to the total energy of (heat change (q) or enthalpy change (△H)
conditions needed to shift the equilibrium. particles: • Heat is positive (q>0) if energy is transferred into
○ Can be summarised in three simple laws • Kinetic energy (Ek) the system
• Potential energy (Ep) The distinction between work and heat is made in the
Problems
surroundings. Energy transferred as:
1. Express the SI units for the following in terms of fundamental units of mass (kg), length (m) and time (s).
a. Force N (Newton) • Heat increases random • Work increases orderly
b. Energy J (Joule) motion in surroundings motion in the surroundings
c. Pressure Pa (Pascal) e.g. weight being raised
2. Calculate the work that a person must do to raise a mass of 1kg through 10m on the surface of:
a. The Earth (g=9.81ms-2)
b. The Moon (g=1.60ms-2)
3. Calculate how much metabolic energy a bird of mass 200g must exert to fly to a height of 20m on the
Earth.
Here the work done is negative
An Ideal Gas as the system drops in energy For example, consider the reaction Zn(s) + 2HCl(aq) => ZnCl2(aq)
• The following criteria are only applicable to the "perfect gas": + H2(g)
○ No intermolecular forces • H2 gas is evolved during the reaction.
○ Negligible molecular size • If performed inside a vessel with a piston, the piston will
○ Collisions are elastic be pushed upwards.
• The pressure of an ideal gas is proportional to T and conc: • Energy is transferred to the surroundings by doing work
and raising a weight. Can measure this energy change
• In terms of numbers of molecules and hence the work done.
• Some energy will also be transferred as heat.
Ideal and Real Gases
• Deriving the gas constant units: • For n moles of ideal gas: pV=nRT
• At constant T (isotherms):
Problems Assume for an ideal gas that • At constant V:
1. Calculate the molar volume (volume per mole, hence n= there are elastic collisions
1) at 298K, 1 bar pressure. Give your answer in m3 and and no intermolecular
dm3. How does this compare with the molar volume at interactions
273K? Purely elastic collisions means T is variable (not dealing with isotherms). When
as things collide there is no sketch P against T at constant V, the gradient is
drop in energy a constant, the graph produces a straight line.
For n moles of a real gas:
• The correction terms:
2. Calculate the value of the Boltzmann constant, kB, and ○ a/V2 increased pressure (as real gases have repulsive forces
give its units. between each other (inelastic collisions))
○ B reduced volume (hence -ve nb. The usable volume is less than the
volume of the container as some of the gas molecules take up that
volume).
• Above the critical temperature a gas cannot be liquified.
3. Using the van der Waals equation for one mole of non- • The critical point is a point of inflexion, hence:
ideal gas, give the SI units of constants a and b.
4. Using the van der Waals equation above, write down expressions for
the first and second differentials of P wrt V at constant temperature.
Expansion Work
• As the gas expands it moves the piston a distance dx against an external
pressure pext, changing the volume dV (from Vinitial to Vfinal)
• The force acting on the piston is If atmospheric pressure
(pressure=force/area) is kept constant then
• Work=force x distance the work is irreversible.
Reversible Expansion
• dw = pextπr2 = -pextdV How to achieve maximum work from the system:
• Therefore Maximum work when external pressure is at a maximum (the greater the opposing force,
the greater the work)
• Expansion gives positive work done External pressure must be less than pressure in system (or compression not expansion)
Expansion against constant pressure
This is irreversible Maximum work obtained when external pressure is infinitesimally less than the pressure of
work at constant the ideal gas in the system
pressure - can't restore (This is reversible work)
system to original For reversible expansion set pext ≈ p at each stage by removing weights from piston
Problem setting • dw = -pdV
1. Calculate the work done (in J) when 1 mole of a gas expands from 5dm3 to • The total work as the system expands from Vi to Vf
10dm3 against a constant pressure of 1 atm is the sum (integral) of all the small steps
Physical Chemistry I Page 1
25 September 2017 15:25
• Thermodynamics is concerned with the study of Work Heat
transformations in energy and the transformation Energy is the capacity to do work • Energy is transferred as heat - the energy of a
of heat into work. It tells us: Work is the motion against an opposing force system changes due to a temperature difference
○ Whether chemical reactions/processes will • Work = force x distance (force = mass x acceleration) between the system and the surroundings.
occur spontaneously or not • The work done is positive (w>0) if energy is • Enthalpy (H) is the "heat content" of a compound
○ Why reactions reach equilibrium, what the transferred into the system. • Often study the change in energy of compounds
composition is at equilibrium, and the There are two contributions to the total energy of (heat change (q) or enthalpy change (△H)
conditions needed to shift the equilibrium. particles: • Heat is positive (q>0) if energy is transferred into
○ Can be summarised in three simple laws • Kinetic energy (Ek) the system
• Potential energy (Ep) The distinction between work and heat is made in the
Problems
surroundings. Energy transferred as:
1. Express the SI units for the following in terms of fundamental units of mass (kg), length (m) and time (s).
a. Force N (Newton) • Heat increases random • Work increases orderly
b. Energy J (Joule) motion in surroundings motion in the surroundings
c. Pressure Pa (Pascal) e.g. weight being raised
2. Calculate the work that a person must do to raise a mass of 1kg through 10m on the surface of:
a. The Earth (g=9.81ms-2)
b. The Moon (g=1.60ms-2)
3. Calculate how much metabolic energy a bird of mass 200g must exert to fly to a height of 20m on the
Earth.
Here the work done is negative
An Ideal Gas as the system drops in energy For example, consider the reaction Zn(s) + 2HCl(aq) => ZnCl2(aq)
• The following criteria are only applicable to the "perfect gas": + H2(g)
○ No intermolecular forces • H2 gas is evolved during the reaction.
○ Negligible molecular size • If performed inside a vessel with a piston, the piston will
○ Collisions are elastic be pushed upwards.
• The pressure of an ideal gas is proportional to T and conc: • Energy is transferred to the surroundings by doing work
and raising a weight. Can measure this energy change
• In terms of numbers of molecules and hence the work done.
• Some energy will also be transferred as heat.
Ideal and Real Gases
• Deriving the gas constant units: • For n moles of ideal gas: pV=nRT
• At constant T (isotherms):
Problems Assume for an ideal gas that • At constant V:
1. Calculate the molar volume (volume per mole, hence n= there are elastic collisions
1) at 298K, 1 bar pressure. Give your answer in m3 and and no intermolecular
dm3. How does this compare with the molar volume at interactions
273K? Purely elastic collisions means T is variable (not dealing with isotherms). When
as things collide there is no sketch P against T at constant V, the gradient is
drop in energy a constant, the graph produces a straight line.
For n moles of a real gas:
• The correction terms:
2. Calculate the value of the Boltzmann constant, kB, and ○ a/V2 increased pressure (as real gases have repulsive forces
give its units. between each other (inelastic collisions))
○ B reduced volume (hence -ve nb. The usable volume is less than the
volume of the container as some of the gas molecules take up that
volume).
• Above the critical temperature a gas cannot be liquified.
3. Using the van der Waals equation for one mole of non- • The critical point is a point of inflexion, hence:
ideal gas, give the SI units of constants a and b.
4. Using the van der Waals equation above, write down expressions for
the first and second differentials of P wrt V at constant temperature.
Expansion Work
• As the gas expands it moves the piston a distance dx against an external
pressure pext, changing the volume dV (from Vinitial to Vfinal)
• The force acting on the piston is If atmospheric pressure
(pressure=force/area) is kept constant then
• Work=force x distance the work is irreversible.
Reversible Expansion
• dw = pextπr2 = -pextdV How to achieve maximum work from the system:
• Therefore Maximum work when external pressure is at a maximum (the greater the opposing force,
the greater the work)
• Expansion gives positive work done External pressure must be less than pressure in system (or compression not expansion)
Expansion against constant pressure
This is irreversible Maximum work obtained when external pressure is infinitesimally less than the pressure of
work at constant the ideal gas in the system
pressure - can't restore (This is reversible work)
system to original For reversible expansion set pext ≈ p at each stage by removing weights from piston
Problem setting • dw = -pdV
1. Calculate the work done (in J) when 1 mole of a gas expands from 5dm3 to • The total work as the system expands from Vi to Vf
10dm3 against a constant pressure of 1 atm is the sum (integral) of all the small steps
Physical Chemistry I Page 1
