An ideal gas is initially at a temperature of 300 K. Its volume triples while its pressure decreases by a factor of two. What is its final temperature?

Question

An ideal gas is initially at a temperature of 300 K. Its volume triples while its pressure decreases by a factor of two. What is its final temperature?

Answer 1

PV=nRT

pV/T=constant

so p goes to 1/2, V goest to 3, so

T=PV/constant=1/2*3/constant looks like T gots to 450K

Answer 2

To solve this problem, we can use the ideal gas law, which states that PV = nRT, 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.

Since we are dealing with an ideal gas, we can assume that the number of moles and the ideal gas constant remain constant.

Let's denote the initial conditions as P₁, V₁, and T₁, and the final conditions as P₂, V₂, and T₂.

According to the problem, we have:
P₂ = P₁/2, since the pressure decreases by a factor of two.
V₂ = 3V₁, since the volume triples.

First, let's find the ratio of the initial and final temperatures using the relationship between pressure and temperature, known as Gay-Lussac's Law. It states that the pressure of an ideal gas is directly proportional to its temperature, assuming constant volume and amount of gas.

P₁/T₁ = P₂/T₂

Substituting the given values, we have:
(P₁/2)/T₁ = P₁/T₂

Simplifying the equation, we get:
2/T₁ = 1/T₂

Now, let's find the ratio of the initial and final temperatures using the relationship between volume and temperature, known as Charles's Law. It states that the volume of an ideal gas is directly proportional to its temperature, assuming constant pressure and amount of gas.

V₁/T₁ = V₂/T₂

Substituting the given values, we have:
3V₁/T₁ = V₁/T₂

Simplifying the equation, we get:
3/T₁ = 1/T₂

Now, we have two equations:
2/T₁ = 1/T₂
3/T₁ = 1/T₂

We can solve these equations simultaneously.

Dividing the second equation by the first equation, we get:
3/2 = T₂/T₂

Simplifying, we get:
3/2 = 1

This implies that T₂ = T₂.

Therefore, the final temperature of the gas remains the same as the initial temperature, which is 300 K.

Answer 3

To find the final temperature of the gas, we can use the ideal gas law, which states that PV = nRT, 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.

In this case, the volume triples, which means V is multiplied by 3. The pressure decreases by a factor of two, which means P is divided by 2. Since the number of moles and the ideal gas constant do not change, we can write the equation as follows:

(P1)(V1) = (P2)(V2)

Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Using the given information, we can substitute the values into the equation:

(P1)(3V1) = (P1/2)(V1)

Now, we can simplify the equation:

3(P1)(V1) = (P1/2)(V1)

Now, we can cancel out V1 from both sides of the equation:

3(P1) = (P1/2)

To solve for P1, we can multiply both sides of the equation by 2:

6(P1) = P1

Now, we can cancel out P1 from both sides of the equation:

6 = 1

This equation does not hold true, which means there is a contradiction in the problem statement. Therefore, it is not possible to determine the final temperature of the gas based on the given information.