Reading Quiz

Question 1:

The First Law of Thermodynamics is given by eq. (1.24) as &DeltaU = Q + W. Discuss the meaning of the various symbols in this relationship. What does it mean if Q is positive or negative? What does it mean if W is positive or negative?

Answer:

&DeltaU is the change in the total energy inside a system. Q is the energy that can be added or removed from the system as heat. Q is the energy that transfers due to a temperature difference; Q > 0 means energy was added to the system in the form of heat, and Q < 0 means energy left the system in the form of heat. W is the work done ON the system by its surroundings. W > 0 means that the work done ON the system by its surroundings increased the energy of the system. W < 0 means that the work done BY the system on its surrounding resulted in a decrease in the energy of the system.
  1. DeltaU is the change in the energy of the system under question. This is assuming that no other kind of energy enters or leaves the system. Q is the heat added, and W is the work done. When Q is positive, this means that heat (arising from differences in temperature) has entered the system, and when negative, heat has left the system (energy has left/entered the system _spontaneously_). Work (W) is positive when work is being done on the system (this is w/o an observer, so no references are made "work done by you" or something) while negative means that works was done by the system on the surroundings.
  2. Delta U is the total change in energy of the system. As heat and work are applied to the system because of conservation of energy the total energy changes. Q is the heat applied to the system and W is the work done. A negative Q or W means that heat leaves the system or that the system does work.
  3. Equation (1.24) is described as, "...the change in energy equals the heat added plus the work done." When Q is positive, heat is added, when negative, heat is lost. Positive W denotes added energy via work being done to the system. Negative W denotes energy is lost via work to another system.
  4. delta U represents the change in the total energy inside the system. Q represents the amount of energy that enters the system as heat and W represents the amount of energy that enters the system as work. If Q is positive energy is being added in the form of heat, if negative, energy is leaving the system in the form of heat. If W is positive energy is entering the system in the form of work, and if W is negative then the system is losing energy by doing work.
  5. the delta U is the change of energy in a system, which is equal to the amount of work done to the system (w)plus the amount of hewat added to a system (Q). If the W is negative that means the system did work on something and if the Q is negative it means that the system lost some heat (or wound up at a colder temp than when it started.
  6. DeltaU is the change in the total energy inside a system. Q is the amount of heat applied to a system, while W is the amount of work done on a system. If Q is positive, it means that heat is added to the system; if negative, heat is being taken out of the system. If W is positive, work is being done on the system; if negative, the system is doing work on the outside world.
  7. delta U is the change in total energy in the system. Q is the heat entering the system (hence it is positive if heat enters the system and negative if heat leaves the system) and W is the work done on the system (with the same sign convention as Q).
  8. deltaU refers to the change in a system's total energy. Changes in U result from movement of heat (q) into or out of the system and by work (W) done on the system. The sign convention used refers to the condition of the system, thus Q is negative when heat leaves the system (positive when it enters) and W is negative when a system performs work and positive when work is done on a system.
  9. Delta U is the total change in energy of a system, Q is the amount of heat entering the system (positive) or leaving the system (negative), and W is the amount of work being done on a system (positive) or the work being done by the system (negative).
  10. U=total energy in a system Q=amount of energy entering a system in the form of heat. W=amount of energy entering a system in the form of work. +Q => Heat entering -Q => Heat leaving +W => Work being done ON system -W => Work being done BY system
  11. delta U is the change in energy, Q is defined by the heat added (negatuve Q is then heat escaping), and W is work done (so negative W is work by the system).

Question 2:

(Problem 1.26) A battery is connected in series to a resistor, which is immersed in water (to prepare a cup of tea). Would you classify the flow of energy from the battery to the resistor as "heat" or "work"? What about the flow of energy from the resistor to the water?

Answer:

When the battery is connected to the resistor, energy flows from the battery to the resistor. If we consider the resistor as our system, the total energy of the resistor increases. However, this energy flow was NOT due to a difference in temperature; in fact, the battery could be much colder than the resistor. So I'd classify this flow of energy as work. However, the increase in the energy of the resistor does result in an increase in temperature, and energy does spontaneously flow from the resistor into the water. I'd classify this flow of energy from the resistor to the water due to a temperature difference as heat.
  1. The flow of energy from batter to resistor is electrical work, since it does not arise from the difference in temperature but differences in potential. Initially you could say everything is at the same temparature. The flow of energy from resistr to water however, would be heat, since the resistor is heated by electrical work and is raised to a higher temperature than the surrounding water and from there energy flows spontaneously.
  2. The energy flowing from the batter to the resistor is work because the energy is a result of electrons being pushed through the resistor. The flow of energy from the resistor to the water is heat because it is just a flow of energy due to temperature differences.
  3. Flow of energy from battery to resistor is work, as the energy transfered is electrical. Flow of energy from the resistor to the water is heat, as the energy transfered is thermal. The resistor converts electrical energy to thermal energy.
  4. The flow of energy from a battery to the resistor is heat. The flow of energy from the resistor to the water is work.
  5. The flow of energy from the battery to the resister is work, where as the flow of energy from the resister to the water is heat.
  6. The flow of energy from the battery to the resistor is work: it acts on electrons, which move and cause the resistor to heat up. The flow of energy from the resistor to the water is heat, for heat flows from the resistor to teh surrounding water through convection.
  7. The flow of energy from the battery to the resistor is caused by a difference in the potential, so it is "work". The flow of energy from the resistor to the water is caused by a difference in the temperature, so it is "heat".
  8. The flow of energy to the resistor is work. The flow of energy to the water is heat because it is spontaneous and caused by a temperature difference.
  9. The battery is doing work on the resistor through the transfer of electrical energy, but the energy is transferred to the water as heat since the transfer occurs spontaneously due to a difference in temperatures.
  10. Battery to resistor would be work because it is not a result of a temperature difference. The flow from resistor to water would be heat.
  11. Energy flow from battery to resistor is work. The energy flow from the resistor to the water is heat.

Question 3:

What's an isothermal process? What's an adiabatic process? Which of these two processes is the (idealized) slow process?

Answer:

An isothermal process is one in which the temperature remains constant. An adiabatic process is one in which no heat enters or leaves the system (Q = 0.) Very slow process are isothermal, because there is enough time for heat to flow in or out until the temperature of the system equilibrates with its surroundings.
  1. An isothermal process is a process that is done slowly _enough_ so that the temperature does not change during the process. (i.e. PV=nRT, T is constant, only P and V change). An adiabatic process is a process that is done fast _enough_ so that no heat leaves the system from changes in temperature.
  2. An isothermal process is one that is so slow the temperature doesn't change. An adiabatic process is one where the process is so fast that no heat escapes. The isothermal process is the slow idealized one.
  3. An isothermal process is one where the temperature remains constant during the process. An adiabatic process is a process where there is a temperature change, but is so speedy that there is no time for the gas to lose thermal energy. The isothermal process is the idealized, slow process.
  4. An isothermal process is a compression which happens so slowly that the temperature does not rise at all. Adiabatic compression is a compression which happens so fast that no heat escapes form the gas during the compression. Isothermal compression is the idealized or slow process.
  5. Isothermal process is the slow process. In iosthermal reactions the gas maintains its temperature (it does not rise), where as in an adibatic process the system loses no heat since it is so quick.
  6. An isothermal process is one which is so slow that the temperature of the gas doesn't rise. An adiabatic process is one that is so fast that no heat escapes from the system. The isothermal process is the slow process.
  7. An isothermal process is one which takes place slow enough that the temperature of the system doesn't change. An adiabatic process is one which takes place fast enough that no heat leaves the system. The isothermal process is the idealized slow process.
  8. An isothermal process occurs without a temperature change and is the most idealized. Adiabatic processes occur without a change in Q and are reasonable estimates of real processes.
  9. An isothermal process is a slow compression of a gas such that the temperature of the gas doesn't rise (it is transferred to the environment). An adiabatic process is a fast compression of a gas such that no heat is transferred between the gas and the environment. The isothermal process is the ideal.
  10. A process in which the temperature of the system is fixed. A process in which the no heat escapes from the system (deltaQ=0) Adiabatic.
  11. These are both idealized versions of the real world. Isothermal means that the process occurs slowly so that the temperature is constant. Adiabatic means the process occurs rapidly so that Q=0.

Question 4:

Which process results in a steeper curve in a P vs. V plot for an ideal gas: an adiabatic process or an isothermal process? Explain briefly.

Answer:

An adiabatic process is always steeper than any isotherm that intersects it. Consider an adiabatic compression, where work is done ON the gas (W > 0), but Q = 0. By the first law, the energy of the gas must increase, which means the temperature of the gas must increase. So you must go from a low temperature to a high temperature. See Figure 1.12 to observe that this means the adiabat must be steeper than any intersecting isotherm.
  1. Since an adiabatic process neads to go from one isotherm to another, it has to be steeper than either isotherm, otherwise it will never reach the final temperature, which we know is possible. (a P vs. V plot is the same for an ideal gas and an isothermal process, since T is constant in such)
  2. The adiabatic process has a steeper curve in the P vs. V plot. This is because it must connect a low and a high temperature isothermal plots and thus must be steeper.
  3. Adiabatic. An adiabat will begin on one isotherm curve and end on a isotherm curve above it. Therefore it must be steeper then an isothermal curve.
  4. An adiabatic process causes a steeper curve in a P vs. V plot for an ideal gas. This is caused by the change in temperature during the process. The Ideal Gas law shows that when temperature is able to increase, it causes a greater change in both P and V causing the steeper curve in the plot.
  5. adibatic processes result in a steeper curve because the pv diagram line must "connect a now temperature isotherm with a high temperature isotherm, and therefore must be steeper."
  6. An adiabatic process has a steeper curve in a P vs. V plot for an ideal gas. The isothermal process stays on a single isotherm and follows only that curve throughout the graph. An adiabatic process jumps in between isotherms, from a lower to a higher one, so its curve is steeper.
  7. An adiabat has a steeper curve, since it connects two different isotherms.
  8. Adiabats are steeper than isotherms because heat is retained by the system and temperature increases. The adiabat connects a low-temperature isotherm to one at a higher temperature.
  9. The adiabatic process involves moving from a lower-temperature isotherm to a higher-temperature isotherm, therefore the adiabat has to be steeper than either of the isotherms.
  10. Adiabat. In an isothermal process heat is allowed to flow in or out of the system in order to keep T constant. However, in the adiabatic case, there is no heat flow in or out of the system and the temperature is allowed to change, which directly effects the slope of the PV curve.
  11. An adiabatic process has a steeper curve because it connects a low-temperature isotherm to a high-temperature isotherm.

Question 5:

What (if any) were the conceptual or mathematical difficulties you had with the reading, or with material from previous classes?

Answer:

Your responses below.
  1. None.
  2. How can the adiabatic process still be considered quasistatic if it has to be really fast so that no heat escapes.
  3. I think it is uncool of Schroeder to write "Let me remind you that tempearature, fundamentally, is a measure of an object's tendency to spontaneously give up energy... but please don't think of this as a definition of temperature" on page 17 when he writes "...let me now restate the theoretical defintion of temperature: Temperature is the a measure of the tendency of an object to spontaneously give up energy to its surroundings" on page 3.
  4. The lines between real-life applications of heat and work were a little blurry.
  5. nope
  6. If, as the song said, "Heat is Work and Work is Heat," then why are they two different concepts in the First Law of Thermodynamics?
  7. These sections were pretty straightforward.
  8. The relationship between PV plots and temperature always confused me.