Thermodynamics

Step 1: State the First Law of Thermodynamics. The first law is often expressed as , where is the change in the internal energy of a system, is the heat added to the system, and is the work done by the system.

Step 2: Interpret the meaning of the law. This law states that the change in a system's internal energy is equal to the heat supplied to the system minus the work done by the system. In essence, it says that energy cannot be created or destroyed, only transferred or changed from one form to another (e.g., from heat into work and internal energy).

Step 3: Relate the interpretation to fundamental conservation principles. The principle that energy cannot be created or destroyed is the law of conservation of energy. Therefore, the First Law of Thermodynamics is a restatement of the conservation of energy principle, specifically applied to thermodynamic systems.

Step 1: Define Boyle's Temperature ( ). Boyle's temperature is the specific temperature at which a real gas behaves most like an ideal gas over a range of pressures. At this temperature, the effects of attractive forces and repulsive forces approximately cancel each other out.

Step 2: Analyze the behavior of a real gas below Boyle's Temperature. Below , the attractive forces between gas molecules are dominant at moderate pressures. An increase in pressure makes it easier for molecules to come together, causing the volume to decrease more than it would for an ideal gas. This makes the product PV decrease initially. At very high pressures, repulsive forces become dominant, causing the volume to be larger than for an ideal gas, and the PV product increases. Thus, the PV vs P curve shows a dip (minimum).

Step 3: Analyze the behavior of a real gas above Boyle's Temperature. Above , the kinetic energy of the molecules is high, and the repulsive forces (due to molecular size) are dominant at all pressures. An increase in pressure results in a PV value that is always greater than that of an ideal gas, and PV continuously increases with P.

Step 4: Evaluate the options. (A) Incorrect. PV first decreases, then increases below . (B) Incorrect. PV continuously increases above . (C) Correct. This accurately describes the behavior below Boyle's temperature, with an initial decrease followed by an increase. (D) Incorrect. PV is constant for an ideal gas, not a real gas above .