A sealed cylinder of gas contains nitrogen gas at 1.00 10e3 kPa pressure and a temperature of 25°C. The cylinder is left in the sun, and the temperature of the gas increases to 60.°C. What is the new pressure in the cylinder?
To find the new pressure in the cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
The problem states that the cylinder is sealed, so the volume remains constant. Therefore, we can rewrite the equation as:
P1/T1 = P2/T2
Where:
P1 = Initial pressure
T1 = Initial temperature
P2 = New pressure (unknown)
T2 = New temperature
Let's plug in the given values into the equation:
P1 = 1.00 x 10^3 kPa
T1 = 25°C = 298 K (Kelvin)
T2 = 60°C = 333 K (Kelvin)
Now, we can rearrange the equation to solve for P2:
P2 = (P1 x T2) / T1
Substituting the values:
P2 = (1.00 x 10^3 kPa x 333 K) / 298 K
P2 = (333 x 10^3 kPa) / 298
P2 ≈ 1116.8 kPa
Therefore, the new pressure in the cylinder is approximately 1116.8 kPa.
(P1/T1) = (P2/T2)
T must be in kelvin.