2.) If the volume of a gas at -73 degrees celcius is doubled while pressure is held constant, what will be its final temperature in degrees celsius?
5.) A gas storage tank at a large industrial plant is designed to provide fuel under constant pressure. When the plant is shut down on friday afternoon, the volume of the tank is 21.5 m^3 at 75 deg. C. If the temp. drops to 30 degC by Monday morning, what volume will the fuel occupy at that time?
2) (V1/T1) = (V2/T2). Remember T must be in kelvin. The problem gives no initial volume except V. You can do either of two things.
a. Assume any number for V1; then V2 will be twice that number.
b. Just call the initial volume V1, then V2 will be 2V1.
5). Same procedure as 2) except you don't need to assume anything.
To answer both questions, we can use the ideal gas law, which states that:
PV = nRT
where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
To solve these problems, we need to convert the given temperatures from Celsius to Kelvin using the conversion formula:
Kelvin = Celsius + 273.15
Now let's solve each question step by step:
2.) If the volume of a gas at -73 degrees Celsius is doubled while the pressure is held constant, we need to find the final temperature in degrees Celsius.
First, convert -73 degrees Celsius to Kelvin:
Temperature in Kelvin = -73 + 273.15 = 200.15 K
Since the pressure is constant, we can rearrange the ideal gas law equation to solve for the final temperature:
T2 = (V2 / V1) * T1
where:
T2 = final temperature in Kelvin
V2 = final volume
V1 = initial volume
T1 = initial temperature in Kelvin
In this case, since the volume is doubled, V2 = 2 * V1. Plugging in the values:
T2 = (2 * V1 / V1) * T1
T2 = 2 * T1
T2 = 2 * 200.15
T2 = 400.30 K
Finally, convert the answer from Kelvin back to degrees Celsius:
Final temperature in Celsius = 400.30 - 273.15 ≈ 127.15 degrees Celsius
Therefore, the final temperature in degrees Celsius is approximately 127.15°C.
5.) To find the volume the fuel will occupy when the temperature drops from 75°C to 30°C, we need to calculate the final volume.
Convert the initial and final temperatures to Kelvin:
Initial temperature in Kelvin = 75 + 273.15 = 348.15 K
Final temperature in Kelvin = 30 + 273.15 = 303.15 K
Since the pressure is constant, we can again use the rearranged ideal gas law equation:
V2 = (T2 / T1) * V1
Plugging in the values:
V2 = (303.15 / 348.15) * 21.5 m^3
Using a calculator, we find:
V2 ≈ 18.68 m^3
Therefore, the volume the fuel will occupy at 30°C is approximately 18.68 m^3.