# Question about deriving Gay-Lussac's Law

• ƒ(x)
In summary, the conversation discusses deriving an equation relating pressure and temperature using only Charles' Law and Boyle's Law. It is mentioned that Gay-Lussac's Law may be useful but ultimately, an equation cannot be found with all three variables using the given laws.
ƒ(x)
There's a flaw in my logic, and I cannot find it.

Ok, all you are allowed to use is Charles' Law (V/T = K) and Boyle's Law (PV = K) and you have to derive an equation relating pressure and temperature.

V = kT
V = k/P
kT = k/P
PT = 1
Therefore P1T1 = P2T2

But, this is the exact opposite of what Gay-Lussac's Law states

Note that V/T = K is only valid for constant pressure, and P V = C is only valid for constant temperature (I think K and C are in general different constants, so let me use different symbols for them).

If you want to vary the pressure, for example, you actually need to write V / T = K(P).
For the Gay-Lussac Law, you need a constant volume (note that the constant quantity is always the one "missing" from the equation, of course that's just because we're sweeping it into the constant on the right hand side).

Though all three (Charles, Boyle and Gay-Lussac) can be easily derived from the ideal gas law,
$$\frac{P V}{T} = \text{constant}$$
I don't immediately see how you can solve your question... I keep getting identities like
$$\frac{P}{T} = \frac{ K(P) C(T) }{ V^2}$$
where K(P) and C(T) are only constants for constant pressure and temperature, respectively.

Compuchip is correct, the K's in the two equations are different, and each K can contain information about whatever quantity is being held constant.

I'm wondering if it's helpful to rewrite the equations as
V = K1T
and
V = K2/P
From there, can the OP come up with an equation with all three variables (and perhaps a different constant K3), eg.
V = K3 x ?

## 1. What is Gay-Lussac's Law and what does it describe?

Gay-Lussac's Law, also known as the Pressure-Temperature Law, is a gas law that describes the relationship between the pressure and temperature of a gas at a constant volume. It states that the pressure of a gas is directly proportional to its temperature when volume is held constant.

## 2. How is Gay-Lussac's Law derived?

Gay-Lussac's Law can be derived from the Ideal Gas Law, which states that the product of pressure and volume is equal to the product of the number of moles of gas, the gas constant, and the temperature. By rearranging this equation and considering a constant volume, we can isolate the relationship between pressure and temperature.

## 3. What is the mathematical equation for Gay-Lussac's Law?

The mathematical equation for Gay-Lussac's Law is P/T = k, where P is the pressure of the gas, T is the temperature of the gas, and k is a constant value. This equation shows that as temperature increases, so does pressure, and vice versa.

## 4. What are the units used in Gay-Lussac's Law?

The units used in Gay-Lussac's Law depend on the units used for pressure and temperature. In SI units, pressure is measured in Pascals (Pa) and temperature is measured in Kelvin (K). However, other units such as atmospheres (atm) and Celsius (°C) can also be used as long as they are consistent.

## 5. How is Gay-Lussac's Law applied in real-life situations?

Gay-Lussac's Law has many practical applications, such as in the operation of internal combustion engines, where an increase in temperature leads to an increase in pressure, resulting in the expansion of gases that drive the engine. It is also important in understanding the behavior of gases in weather systems and in the production of compressed gases for industrial and medical purposes.

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The text passage discusses the derivation of an equation relating pressure and temperature using Charles' Law and Boyle's Law, and it includes a series of questions and answers about Gay-Lussac's Law.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Question about deriving Gay-Lussac's Law

• ƒ(x)
In summary, the conversation discusses deriving an equation relating pressure and temperature using only Charles' Law and Boyle's Law. It is mentioned that Gay-Lussac's Law may be useful but ultimately, an equation cannot be found with all three variables using the given laws.
ƒ(x)
There's a flaw in my logic, and I cannot find it.

Ok, all you are allowed to use is Charles' Law (V/T = K) and Boyle's Law (PV = K) and you have to derive an equation relating pressure and temperature.

V = kT
V = k/P
kT = k/P
PT = 1
Therefore P1T1 = P2T2

But, this is the exact opposite of what Gay-Lussac's Law states

Note that V/T = K is only valid for constant pressure, and P V = C is only valid for constant temperature (I think K and C are in general different constants, so let me use different symbols for them).

If you want to vary the pressure, for example, you actually need to write V / T = K(P).
For the Gay-Lussac Law, you need a constant volume (note that the constant quantity is always the one "missing" from the equation, of course that's just because we're sweeping it into the constant on the right hand side).

Though all three (Charles, Boyle and Gay-Lussac) can be easily derived from the ideal gas law,
$$\frac{P V}{T} = \text{constant}$$
I don't immediately see how you can solve your question... I keep getting identities like
$$\frac{P}{T} = \frac{ K(P) C(T) }{ V^2}$$
where K(P) and C(T) are only constants for constant pressure and temperature, respectively.

Compuchip is correct, the K's in the two equations are different, and each K can contain information about whatever quantity is being held constant.

I'm wondering if it's helpful to rewrite the equations as
V = K1T
and
V = K2/P
From there, can the OP come up with an equation with all three variables (and perhaps a different constant K3), eg.
V = K3 x ?

## 1. What is Gay-Lussac's Law and what does it describe?

Gay-Lussac's Law, also known as the Pressure-Temperature Law, is a gas law that describes the relationship between the pressure and temperature of a gas at a constant volume. It states that the pressure of a gas is directly proportional to its temperature when volume is held constant.

## 2. How is Gay-Lussac's Law derived?

Gay-Lussac's Law can be derived from the Ideal Gas Law, which states that the product of pressure and volume is equal to the product of the number of moles of gas, the gas constant, and the temperature. By rearranging this equation and considering a constant volume, we can isolate the relationship between pressure and temperature.

## 3. What is the mathematical equation for Gay-Lussac's Law?

The mathematical equation for Gay-Lussac's Law is P/T = k, where P is the pressure of the gas, T is the temperature of the gas, and k is a constant value. This equation shows that as temperature increases, so does pressure, and vice versa.

## 4. What are the units used in Gay-Lussac's Law?

The units used in Gay-Lussac's Law depend on the units used for pressure and temperature. In SI units, pressure is measured in Pascals (Pa) and temperature is measured in Kelvin (K). However, other units such as atmospheres (atm) and Celsius (°C) can also be used as long as they are consistent.

## 5. How is Gay-Lussac's Law applied in real-life situations?

Gay-Lussac's Law has many practical applications, such as in the operation of internal combustion engines, where an increase in temperature leads to an increase in pressure, resulting in the expansion of gases that drive the engine. It is also important in understanding the behavior of gases in weather systems and in the production of compressed gases for industrial and medical purposes.

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user
The text passage discusses the derivation of an equation relating pressure and temperature using Charles' Law and Boyle's Law, and it includes a series of questions and answers about Gay-Lussac's Law.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS