In a closed container, the temperature is doubled. What will happen to the pressure?
Question
In a closed container, the temperature is doubled. What will happen to the pressure?
Solution 1
The question is referring to Gay-Lussac's Law in thermodynamics, which states that the pressure of a gas is directly proportional to its absolute temperature, provided the volume is kept constant.
Here are the steps to understand what happens when the temperature is doubled:
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Initially, let's assume the pressure of the gas in the container is P1 and the temperature is T1.
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According to the problem, the temperature is doubled. So, the new temperature, T2, is 2*T1.
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According to Gay-Lussac's Law, the initial pressure and temperature (P1 and T1) and the final pressure and temperature (P2 and T2) have the following relationship: P1/T1 = P2/T2.
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Substituting T2 = 2T1 in the equation, we get P1/T1 = P2/(2T1).
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Simplifying this equation gives us P2 = 2*P1.
So, if the temperature is doubled in a closed container, the pressure will also double, assuming the volume remains constant.
Solution 2
The question is referring to Gay-Lussac's Law in thermodynamics, which states that the pressure of a gas is directly proportional to its absolute temperature, provided the volume is kept constant.
Here are the steps to understand what happens when the temperature is doubled:
-
Initially, let's assume the pressure of the gas in the container is P1 and the temperature is T1.
-
According to the problem, the temperature is doubled. So, the new temperature, T2, is 2*T1.
-
According to Gay-Lussac's Law, the initial pressure and temperature (P1 and T1) and the final pressure and temperature (P2 and T2) have the following relationship: P1/T1 = P2/T2.
-
Substituting T2 = 2T1 in the equation, we get P1/T1 = P2/(2T1).
-
Simplifying this equation gives us P2 = 2*P1.
So, if the temperature is doubled in a closed container, the pressure will also double, assuming the volume remains constant.
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