A soda can with 120,000 PA of pressure is heated from 240 K to 300 K in hot water. What is the new pressure in the can
To find the new pressure in the can, we can make use of the ideal gas law:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = gas constant
T = temperature
Since the volume of the soda can remains constant and we are looking for the new pressure, we can rewrite the equation as:
P1/T1 = P2/T2
Where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure (what we want to find)
T2 = final temperature
Substituting the given values into the equation:
P1 = 120,000 Pa (initial pressure)
T1 = 240 K (initial temperature)
T2 = 300 K (final temperature)
P1/T1 = P2/T2
120,000/240 = P2/300
P2 = (120,000/240) * 300
P2 = 150,000 Pa
Therefore, the new pressure in the can is 150,000 Pa.
To find the new pressure in the soda can, you can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we want to find)
V2 = final volume (since the volume of the can remains constant, V2 is the same as V1)
T2 = final temperature
In this case, we are given the initial pressure (P1 = 120,000 Pa), the initial temperature (T1 = 240 K), and the final temperature (T2 = 300 K). We need to solve for the final pressure (P2).
Since the volume of the can remains constant, we can eliminate the volume terms from the equation:
P1 / T1 = P2 / T2
Now, we can plug in the given values:
(120,000 Pa) / (240 K) = P2 / (300 K)
To find P2, we can rearrange the equation:
P2 = (120,000 Pa) * (300 K) / (240 K)
Calculating this, we get:
P2 = 150,000 Pa
Thus, the new pressure inside the can is 150,000 Pa.
To find the new pressure in the can after heating, we can use the combined gas law.
The combined gas law is represented by the formula:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we need to find)
V2 = final volume (assuming the volume remains constant)
T2 = final temperature
In this case, we are given:
P1 = 120,000 Pa
T1 = 240 K
T2 = 300 K
Assuming the volume remains constant, we can rearrange the formula to solve for P2:
P2 = (P1 * T2) / T1
Substituting the given values:
P2 = (120,000 * 300) / 240
P2 ≈ 150,000 Pa
Therefore, the new pressure in the can after heating is approximately 150,000 Pa.