A cylinder of propane gas at a temperature of 20 C exerts a pressure of 8 atm. When a cylinder has been placed in sunlight, its temperature increases to 25 C . What is the pressure of the gas inside the cylinder at this temperature?
the pressure is proportional to the absolute (Kelvin) temperature
[(25 + 273) / (20 + 273)] * 8 atm
To find the pressure of the gas inside the cylinder at the increased temperature, you will need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas (assumed to be constant for this problem)
n = number of moles of the gas (assumed to be constant for this problem)
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas in kelvin
First, convert the given temperatures from Celsius to Kelvin:
T1 = 20 + 273 = 293 K (initial temperature)
T2 = 25 + 273 = 298 K (final temperature)
Since the volume and moles of the gas are assumed to be constant, they can be canceled out in the equation.
Now, rearrange the equation to solve for the final pressure (P2):
P1/T1 = P2/T2
Substitute the known values into the equation:
8 atm / 293 K = P2 / 298 K
Now, solve for P2:
P2 = (8 atm * 298 K) / 293 K
P2 ≈ 8.14 atm
Therefore, the pressure of the propane gas inside the cylinder, when the temperature increases to 25°C, is approximately 8.14 atm.
To find the pressure of the gas inside the cylinder at the increased temperature, you can use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure of the gas (in atm),
V is the volume of the gas (in liters),
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature of the gas (in Kelvin).
Given:
Initial temperature (T1) = 20°C
Pressure at T1 = 8 atm
Final temperature (T2) = 25°C
To solve the problem, we need to convert the temperatures from Celsius to Kelvin:
T1 = 20°C + 273.15 = 293.15 K
T2 = 25°C + 273.15 = 298.15 K
Let's assume the volume and the number of moles of the gas remain constant. Thus, we can rewrite the equation as:
P1/T1 = P2/T2
Now, plug in the given values:
8 atm/293.15 K = P2/298.15 K
To find P2, we can rearrange the equation:
P2 = (8 atm * 298.15 K) / 293.15 K
Simplifying the equation further, we get:
P2 = 8.13 atm
Therefore, the pressure of the gas inside the cylinder at the increased temperature of 25°C is approximately 8.13 atm.