Final answer:
The temperature is not always uniquely determined by pressure and volume alone; other factors like the amount of gas and its nature must be constant. Thus, the answer is 'No' (Option B).
Step-by-step explanation:
This is because the only way the temperature would be uniquely determined is if the amount of gas and the nature of the gas in the system remain constant, which is not specified in the question. This principle is derived from the Ideal Gas Law (PV=nRT), where P is pressure, V is volume, T is temperature, n is the amount of gas, and R is the gas constant.
Furthermore, according to Gay-Lussac's Law, when pressure is constant, volume is directly proportional to temperature. Similarly, Charles's Law states that when the temperature remains constant, the volume and pressure of a gas are inversely proportional. When heat adds energy to a gas, the pressure and volume of the system will likely change according to these gas laws.
To illustrate, let's assume we have a sealed container with a fixed amount of gas at a constant volume. If heat is transferred to this container, the pressure would increase while the temperature also increases, unless the amount of gas changes, which would disrupt the straightforward relation between pressure, volume, and temperature.
Thus, the correct option is B.