Physics II

• What is special about the change in the state function called enthalpy?

  for a process taking place at constant pressure, the change in enthalpy gives the heat added to the system, or delta H = Q
• What is important about the change in the state function called internal energy?

  for a process taking place at constant volume, the change in the energy is equal to the heat added to the system, or delta U = Q
• What is an isothermal process?

  This is a process that takes place at constant temperature. The final temperature of the system is equal to the initial temperature of the system
• What is an adiabatic process?

  a process that takes place in an insulated container so that no heat is exchanged with the surroundings
• What is an isobaric process?

  a process that takes place at constant pressure
• What is an isochoric process?

  a process that takes place at constant volume
• What four steps make up the thermodynamic cycle of the Stirling engine?

  Isothermal (constant T) expansion at Thot, Isochoric (constant V) cooling to Tcold, Isothermal compression at Tcold, Isochoric heating back to Thot
• What four steps make up the thermodynamic cycle of the Carnot engine?

  Isothermal reversible expansion at Thot, adiabatic reversible expansion to lower the temperature at Tcold, isothermal reversible compression at Tcold, and adiabatic reversible compression to raise the temperature back to Thot
• What is the difference between a reversible process and an irreversible process?

  Reversible process: takes place slowly so that the system is not taken out of equilibrium (would not take place in any finite amount of time)

  irreversible process: takes place quickly so that the system is taken out of equilibrium
• The surroundings are always assumed to take on heat in a reversible fashion. Why?

  the surroundings is the "rest of the universe", an infinite reservoir. When any finite amount of heat from the system is spread throughout the surroundings, the perturbation to the state of the surroundings is negligible. Hence the surroundings remains in equilibrium
• What postulate concerning energy forms the basis of the first law of thermodynamics?


  The energy of the universe remains constant
• What is the efficiency of a Carnot cycle running between a cold reservoir at Tc and a hot reservoir at TH?

  efficiency = (Th - Tc)/Th
• True or False: All reversible heat engines operating between two heat reservoirs have the same efficiency?

  True. They all have the Carnot efficiency
• What is the efficiency if the working fluid is some other non-ideal gas?

  The efficiency is the same, regardless of the working fluid
• True or False: If a piston expands irreversibly, it is impossible to calculate the work b/c it is impossible to determine the integral of PdV b/c we have no way of assigning P to a system out of equilibrium?

  False. Even if we can't define the equilibrium pressure of the gas, we can still measure the external pressure on the piston as a function of volume, in principle. The work is the integral of PextdV
• What is the relation between P and V for a reversible isothermal expansion of an ideal gas?

  P=nRT/V
• What is the relation between P and V for a reversible adiabatic expansion of an ideal gas?

  P=const./V^gamma, gamma=Cp/Cv
• True or False: The energy of an ideal gas is given by the following expression: U=Cv*T?

  True. The energy of an ideal gas is a function of temperature only. Since the derivative of U with respect to T is equal to Cv it follows that Cv is the proportionality constant between U and T
• What mathematical relation is regarded as a formal statement of the first law of thermodynamics?

  Delta U= Q-W
• What convention do we follow: Is (a) Q the heat added to the system from the surroundings, or is (b) Q the heat passed to the surroundings from the system?

  Q is the heat added to the system from the surroundings. Thus, Q is positive if the heat is transferred to the system from the surroundings, and Q is negative if the heat is transferred from the system to the surroundings.
• What convention do we follow: is (a) W the work done on the system by the surroundings, or is (b) W the work done on the surroundings by the system?

  W is the work done on the surroundings by the system. If the system does work on the surroundings, W is positive. If the surroundings do work on the system, W is negative
• In thermodynamics we talk about the system and the surroundings. What is the system and what is the surroundings?

  system: the part of the universe on which we are focusing our attention

  surroundings: the rest of the universe
• The first law is said to be a postulate consisting of two parts. What are these two parts?

  The first part of the first law is the postulate that the energy of the universe never changes. The second part is the postulate that energy U is a state function
• Reversible work is performed when the difference between the pressure of the system and the pressure of the surroundings is infinitessimal. What is the analogous requirement on temperature so that heat is transferred reversibly?

  There should be an infinitessimal difference between the temperature of the system and the temperature of the surroundings in order to keep the system in equilibrium. (The surroundings always stays in equilibrium because of its vast size)
• True or False: The state of a system is entirely determined by the specification of just two state variables?

  True. For example, if you specify V and T for an ideal gas, then you can figure out P from the equation of state. You can also figure out U since U is Cv*T
• For an ideal gas, find an expression for the following quantity: (dP/dT)V?

  nR/V
• What is the heat capacity at constant volume for an ideal gas consisting of diatomic molecules (ex: dilute nitrogen or oxygen)?

  Cv=5/2nR
• What is the relation between the heat capacity at constant pressure and the heat capacity at constant volume for an ideal gas?

  Cp=Cv+nR
• True or False: It can be proved that the heat capacity at constant pressure is greater than the heat capacity at constant volume, regardless of the substance?

  True
• The energy of a certain real (non-ideal) gas is given by U=3/2nRT-a(n^2)/V. Calculate the coefficients of an expansion of U(T,V) in the variables T and V?

  dU=(dU/dT)V dT + (dU/dV)T dV

  (dU/dT)V = 3/2 nR

  (dU/dV)T = a (n^2)/(v^2)
• The energy of a certain real gas is given by U=3/2nRT - a(n^2)/V. What is the heat capacity at constant volume?

  Cv=(dU/dT)V= 3/2 nR
• The energy of a certain real gas is given by U=3/2nRT-a(n^2)/V. The equation of state for the gas is PV=nRT-a(n^2)/V. Find the enthalpy H(T,V) as a function of T and V?

  Remember the definition: H=U+PV

  = 5/2 nRT-2a(n^2)/V
• Who showed that the energy of an ideal gas depends only on its temperature; They also measured the dependence of U with V for real gases?

  James Joule and William Thomson (later Lord Kelvin)
• Who patented a heat engine in 1816, for the purpose of powering underwater torpedos without leaving a trail of bubbles?

  Robert Stirling, 1816
• Who devised a hypothetical heat engine that could be run reversibly between two heat reservoirs, one reservoir kept at a hot temperature, the other at a cold temperature?

  Sadi Carnot, 1820
• Who is credited with figuring out the second law of thermodynamics?

  Rudolph Clausius, 1850
• Who investigated the properties of gases and found that at constant temperature, the pressure is inversely proportional to the volume?

  Robert Boyle, 1662
• Who investigated the properties of gases and found that at constant pressure, the volume is proportional to the temperature?

  Jacques Charles, 1787
• Why is it considered bad form to write dQ and dW when referring to small amounts of heat and small amounts of work?

  In calculus, the differential "d" implies a change. Heat Q and work W are quantities that are exchanged between system and surroundings. While their exchange causes a change in U, it makes no sense to talk about a change in the quantity exchanged
• True or False: the entropy S is a state function. It is sometimes related to heat and sometimes not. It is related to heat when heat is transferred reversibly?

  True