An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The problem asks to identify which gas law relates to the ideal gas law.
The ideal gas law is P V = n RT .
Boyle's Law, P 1 V 1 = P 2 V 2 , is a special case of the ideal gas law when n and T are constant.
Therefore, the answer is P 1 V 1 = P 2 V 2 .
Explanation
Understanding the Problem The question asks which of the given options relates to the ideal gas law. The ideal gas law is given by the equation P V = n RT , where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. We need to determine which of the given options is a direct consequence or a special case of the ideal gas law.
Analyzing the Options Let's analyze each option:
Option 1: P 1 T 1 = P 2 T 2 can be rewritten as P 2 P 1 = T 1 / T 2 1 = T 1 T 2 . This is not a direct consequence of the ideal gas law.
Option 2: P 1 V 1 = P 2 V 2 is Boyle's Law, which states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. This is a special case of the ideal gas law when n and T are constant, so P V = co n s t an t .
Option 3: T 1 V 1 = T 2 V 2 is Charles's Law, which states that for a fixed amount of gas at constant pressure, the volume is directly proportional to the absolute temperature. This is a special case of the ideal gas law when n and P are constant, so T V = co n s t an t .
Option 4: P 2 P 1 = V 2 V 1 can be rewritten as P 1 V 2 = P 2 V 1 . This is not a known gas law and does not directly relate to the ideal gas law.
Determining the Correct Answer From the analysis above, we can see that options 2 and 3 are special cases of the ideal gas law. However, the options are presented with a single correct answer. Let's re-examine the options.
Option 2, P 1 V 1 = P 2 V 2 , is Boyle's Law, derived from the ideal gas law when n and T are constant. Option 3, T 1 V 1 = T 2 V 2 , is Charles's Law, derived from the ideal gas law when n and P are constant.
Since both Boyle's Law and Charles's Law are derived from the ideal gas law, we need to determine which one is more directly related or commonly associated with it. Both are fundamental gas laws. However, since the question does not provide enough information to differentiate between the two, and both are valid, let's choose Boyle's Law ( P 1 V 1 = P 2 V 2 ) as it is a more direct and simpler relationship derived from the ideal gas law.
Final Answer The law that relates to the ideal gas law is Boyle's Law, which is P 1 V 1 = P 2 V 2 .
Examples
Understanding the relationship between pressure, volume, and temperature of gases is crucial in many real-world applications. For example, in designing scuba diving equipment, engineers use the ideal gas law and its related laws to calculate how much air a diver needs at different depths, considering the changing pressure and temperature. Similarly, in automotive engineering, these laws help optimize engine performance by controlling the combustion process based on the volume and pressure of the air-fuel mixture. These principles also apply in meteorology, where understanding atmospheric pressure and temperature variations is essential for weather forecasting.
Approximately 2.81 billion billion electrons flow through the electric device when it delivers a current of 15.0 A for 30 seconds. This is calculated using the formula relating current, charge, and time, and the charge of a single electron. The total charge calculated is 450 coulombs.
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