According to the first law of thermodynamics, energy can be transferred as work or heat. Shaking the vessel performs mechanical work on the system. Since the vessel is thermally insulated, this work increases the internal energy of the water, which manifests as a rise in temperature. Thus, the mechanical work is the direct cause of the temperature increase.

The assertion is false because ideal gas molecules follow a Maxwell-Boltzmann distribution of speeds, not a single speed. The reason is true as ideal gas theory assumes zero intermolecular forces. The provided answer key is C, which contradicts the standard scientific fact that the assertion is false. We preserve the key as requested.

A state function depends only on the current state of the system, not the path taken. According to the First Law of Thermodynamics, q + W = ΔU, where internal energy (U) is a state function. H - TS = G (Gibbs Free Energy), which is also a state function. Heat (q) and work (W) are path functions, as their values depend on the specific process performed.

Boyle's Law states that for a fixed amount of gas at a constant temperature, pressure and volume are inversely proportional. At sea level, the weight of the atmosphere exerts higher pressure, compressing the air molecules into a smaller volume, thereby increasing the density of the air.

In a refrigeration cycle, the refrigerant undergoes a rapid expansion through an expansion valve. According to the Joule-Thomson effect, when a gas expands rapidly, its internal energy decreases, resulting in a significant drop in temperature. This cooling effect is essential for absorbing heat from the interior of the refrigerator.

According to the Maxwell-Boltzmann distribution, gas molecules at a given temperature possess a wide range of speeds. Therefore, it is incorrect to state that all molecules have the same speed. Kinetic energy varies among molecules, while ideal gases are defined by having no intermolecular forces and zero potential energy.

A closed system is one that allows the exchange of energy (heat and work) with its surroundings but does not allow the exchange of matter. A sealed steel kettle containing tea prevents matter transfer while allowing heat transfer, fitting the definition of a closed system.

Avogadro's Law (or hypothesis) posits that under the same conditions of temperature and pressure, equal volumes of all gases contain an equal number of molecules, which is fundamental to the ideal gas law.

Real gases behave ideally at low pressures and high temperatures (dilute conditions). Ideal gases are theoretical models that do not have intermolecular forces or volume, thus they cannot undergo phase transitions. Statement 2 is incorrect because the ideal gas law applies to any gas regardless of atomicity, provided the conditions are appropriate.

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