Textbook Question
Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following? (a) Halve the Kelvin temperature while holding the pressure constant
Ch.10 - Gases: Their Properties & Behavior
Chapter 10, Problem 49d
Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following? (d) Double the Kelvin temperature and double the pressure
Verified step by step guidance1
Step 1: Understand the relationship between pressure, volume, and temperature in a gas. This relationship is described by the ideal gas law, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Step 2: In this problem, we are doubling both the pressure (P) and the temperature (T). We can express this change in terms of the initial and final states of the gas. Let's denote the initial pressure as P1, the final pressure as P2, the initial temperature as T1, and the final temperature as T2. According to the problem, P2 = 2P1 and T2 = 2T1.
Step 3: Substitute these expressions into the ideal gas law for the initial and final states. The initial state is P1V1 = nRT1 and the final state is P2V2 = nRT2.
Step 4: Since the number of moles of gas and the ideal gas constant remain the same, we can set the two equations equal to each other and solve for the final volume V2. This gives us (P1V1)/T1 = (P2V2)/T2.
Step 5: Substitute P2 = 2P1 and T2 = 2T1 into the equation and solve for V2. This will give you the relationship between the initial and final volumes of the gas.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas. In this equation, n is the number of moles of gas, and R is the universal gas constant. Understanding this law is crucial for predicting how changes in temperature and pressure affect gas volume.
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Ideal Gas Law Formula
Charles's Law
Charles's Law states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin) when pressure is held constant. This means that if the temperature of a gas increases, its volume will also increase, provided the pressure does not change. This concept is essential for understanding the effects of temperature changes on gas volume.
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Boyle's Law
Boyle's Law states that the volume of a gas is inversely proportional to its pressure when temperature is held constant. This means that if the pressure of a gas increases, its volume decreases, and vice versa. This principle is important for analyzing how simultaneous changes in pressure and temperature can affect the volume of gas in a cylinder.
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Related Practice
Textbook Question
Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following? (b) Increase the amount of gas by one-fourth while holding the temperature and pressure constant
Textbook Question
Which sample contains more molecules: 1.00 L of O2 at STP, 1.00 L of air at STP, or 1.00 L of H2 at STP?