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**If heat is flowing into a system and work is done by a system, what are the signs of the Q and W associated with this system?**

A. Q and W are positive.

B. Q is positive. W is negative.

C. Q is negative. W is positive.

D. Q and W are negative.

When heat is flowing into the system, Q is positive. When work is done by a system, it is negative. A is incorrect because it describes a system where work is done on a system, not by the system. C and D are incorrect because they describe heat flowing out of the system, not into the system.

The thermodynamic laws refer to things called systems and surroundings, but what exactly are those? A thermodynamic system is tricky to define, because it is essentially whatever we define it to be for a given problem. We could say our system of interest is an organism, a container of gas, or even a car. By definition, anything that is not the system is called the surroundings. The conservation of energy theorem suggests that energy is neither created or destroyed. Therefore, if we measure the energy of a system to increase or decrease, energy must have been gained from or lost to the surroundings, respectively.

The transfer of energy between a system and its surroundings can be described by the transfer of heat and work. An equation describing this is ∆E = Q + W, where ∆E represents the gain or loss of energy in a system. Temperature is proportional to the energy of molecules in a system, so temperature can be measured to determine whether a system gains or loses energy. Q stands for heat and W stands for work. Heat can flow into a system, which we define as positive Q, or out of a system, which is negative Q. Work doesn’t *flow* like heat. Instead, a change in the work of a system involves a change in the volume of the system.

If the volume of a system is increasing, the molecules in the system are pushing against the walls of their container to expand the system. Therefore, the molecules are giving off energy, and the system has an overall decrease in energy. If the volume decreases, something external to the system is pushing against the system to compress it. Therefore, by the surroundings acting to compress the system, the system experiences an overall increase in energy. If the system is decreasing in volume and gaining energy, we can say the system experienced positive work (+W)

When heat and work are changing in a system, the pressure and volume of the system are going to be directly affected. We can represent these differences using a pressure volume diagram, of which there are four different types, depending on the type of process that has occurred: isobaric, isochoric, isothermal, or adiabatic. A pressure volume diagram has volume on its x-axis and pressure on its y-axis.

If we want to determine the work done on a system, we need to calculate the area under the curve on a PV diagram. Work is equal to the force applied to an object over a distance, and force is equal to the pressure applied over an area. By combining the ideas in these equations, we find that work on a system is equal to the pressure applied to it divided by its volume (W = P x ΔV). Notice that this equation provides the area under the curve of a PV diagram, which is why calculating this is our method for determining the work done on a system.

*Isobaric Processes*

An isobaric process is a process that occurs under constant pressure. For example, consider a piston with gas molecules inside. If heat flows into the system, then the gas molecules inside the system are moving faster and exerting a greater pressure on the container walls. The greater pressure inside will push the piston up, increasing the volume of the system. This process on a PV diagram is represented by a horizontal line.

Isochoric processes are those that occur with a constant volume. If volume is unable to change, no work can be performed on the system. By process of elimination, any change in the energy of a system must be due to heat added to or released from the system. On a PV curve, since volume is a constant, these processes are represented by a vertical line with no area under the curve.

Isothermal Processes

Isothermal processes are those which occur at a constant temperature. Temperature is directly proportional to the energy of the system, so the energy of the system must not change (ΔE = 0 and Q + W = 0). In other words, any heat added to the system must be compensated for by the system doing work.

We can consider several instances of isothermal systems where temperature doesn’t change. For instance, if the volume increases but temperature doesn’t, molecules are still moving with the same speed as before, but have more distance to travel between collisions. Therefore, the number of collisions between gas molecules and the container walls goes down, decreasing the pressure of the system. Therefore, if volume increases, pressure has to decrease. This relationship calls back to an equation you should remember, PV = nRT. If the moles of gas and the temperature of a system are constant, the pressure and volume of the system will be inversely proportional to one another.

A consequence of this relationship is that the graph of an isothermal system is a curved line, called an isotherm. If an isothermal system is at a higher temperature, an isotherm will be drawn farther up and to the right, as a consequence of the product of pressure and volume being greater (PV ~ T).

Adiabatic processes are those that occur with no heat transfer. If heat transfer cannot occur, any energy transferred to or from the system is due to the effects of work (ΔE = W). As a consequence, if work is done on the system, the system must gain energy and will increase in temperature. If work is done by the system, the system must lose energy and will decrease in temperature. If the volume of an adiabatic system increases, there is a correspondingly large decrease in pressure, which is much more significant than in an isothermal process.

In an isothermal process, when the volume expands, molecules are still moving at the same speed. Pressure drops because it takes longer for molecules to get from one side of the container to the other side of the container. In an adiabatic process, if volume increases, it’s because the system did work to push the volume larger, expending energy and decreasing in temperature. Therefore, the volume of the system increased and the molecules are moving slower. This double whammy means that the rate of collisions and strength of collisions after an adiabatic process where volume decreases is much more significant than in an isothermal process. Therefore, a PV curve of an adiabatic process is steeper than an isotherm.

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