Thermodynamics

Step 1: Analyze each statement. - A. Specific heat of saturated water vapour at 100 C is negative: Saturated vapor is vapor in equilibrium with its liquid phase. If you add heat to saturated steam, it will superheat, and to keep it saturated, you must compress it. This compression work increases the temperature more than the added heat, so to maintain a constant temperature, you would actually have to remove heat. Alternatively, if you expand saturated steam adiabatically (no heat exchange), it cools and condenses. To prevent condensation and keep it saturated during expansion, you must add heat. The specific heat is defined per unit temperature change, and under certain processes for saturated steam, it can indeed be negative. So, A is correct. - B. There is only one triple point of a substance: The triple point is the unique combination of temperature and pressure at which the solid, liquid, and gas phases of a substance can all coexist in thermodynamic equilibrium. For a pure substance, this is a unique, fixed point. So, B is correct. - C. Boiling point of every liquid rises with increase in pressure: The boiling point is the temperature at which the vapor pressure of a liquid equals the surrounding pressure. For all liquids, vapor pressure increases with temperature. Therefore, to make the liquid boil at a higher temperature, you must increase the external pressure. So, C is correct. - D. Latent heat can not become zero: The latent heat of vaporization is the energy required to change a substance from liquid to gas at constant temperature and pressure. As you increase the temperature and pressure along the boiling curve, you approach the critical point. At the critical point, the distinction between liquid and gas phases disappears, and the latent heat of vaporization becomes zero. So, D is incorrect.
Step 2: Conclude the set of correct statements. Statements A, B, and C are correct.

The Law of Dulong and Petit is a classical thermodynamic law that describes the molar specific heat capacity of a solid element. It is based on the classical equipartition theorem. The law states that, at sufficiently high temperatures, the molar specific heat at constant volume ( ) for all solid elements is approximately constant and equal to , where is the universal gas constant. "Atomic heat" is another term for molar specific heat. The law predicts this value to be constant, independent of the substance and temperature (at high temperatures). While modern quantum theories (like the Debye model) show that the specific heat does decrease and approach zero at absolute zero, the classical law of Dulong and Petit itself predicts a constant value. The question asks what the law states, not what is observed experimentally at low temperatures.

The specific heat of saturated water vapor is a non-intuitive concept. Saturated vapor is vapor that is in equilibrium with its liquid phase (i.e., it's on the point of condensing). Consider a process where we add heat to saturated water vapor. This added heat will tend to increase its temperature (superheat it). However, to keep the vapor in a saturated state at this new, higher temperature, the pressure must also increase significantly along the vaporization curve. To achieve this higher pressure, the vapor must be compressed. The work done on the vapor during this compression can increase its internal energy (and thus temperature) by more than the amount of heat added. In order to only reach the new saturation temperature without overshooting it, heat must actually be removed from the system. Since specific heat is defined as the heat added per unit mass per unit temperature change ( ), and in this process can be negative while is positive, the specific heat of saturated water vapor is negative.

Step 1: Recall the two forms of the ideal gas law. - The molar form is , where is the number of moles and is the universal gas constant. - The molecular form is , where is the number of molecules and is the Boltzmann constant.
Step 2: Relate the number of moles ( ) to the number of molecules ( ). The number of molecules is equal to the number of moles multiplied by Avogadro's number ( ), which is the number of molecules per mole.
Step 3: Equate the two forms of the ideal gas law and solve for R. Substitute : Cancel and from both sides: Thus, the universal gas constant is the product of Avogadro's number and the Boltzmann constant.

Concept: An adiabatic process is a thermodynamic process in which no heat is exchanged between the system and its surroundings. For an ideal gas undergoing an adiabatic process, the relation between pressure and volume is given by where

• = pressure
• = volume
• = adiabatic index

Step 1: Use the first law of thermodynamics.} For adiabatic process
Step 2: Derive the pressure–volume relation.} Using ideal gas relations and thermodynamic identities, the final relation becomes
Step 3: Interpretation.} During adiabatic expansion, volume increases and pressure decreases more rapidly compared to an isothermal process. Thus, the correct relation is