a sealed cylinder of a gas contains nitrogen gas at 1.00*10^3 kPa pressure and a temperature of 20C. They cylinder is left in the sun and the temperature of the gas increases to 50C. What is the new pressure in the cylinder?
To find the new pressure in the cylinder, we can use the ideal gas law equation:
P₁V₁/T₁ = P₂V₂/T₂
Where:
P₁ = initial pressure of the gas
V₁ = volume of the gas (which remains constant)
T₁ = initial temperature of the gas
P₂ = new pressure of the gas (to be determined)
V₂ = same volume of the gas
T₂ = new temperature of the gas
In this case, we are given P₁ = 1.00*10^3 kPa, T₁ = 20°C (which needs to be converted to Kelvin), T₂ = 50°C (which also needs to be converted to Kelvin), and we assume that the volume (V₁ and V₂) remains constant.
Let's begin by converting the temperatures to Kelvin:
T₁ = 20°C + 273.15 = 293.15 K
T₂ = 50°C + 273.15 = 323.15 K
Now we can substitute the values into the ideal gas law equation:
P₁V₁/T₁ = P₂V₂/T₂
Since V₁ and V₂ are equal and constant, we can cancel them out:
P₁/T₁ = P₂/T₂
Now we can solve for P₂ by rearranging the equation:
P₂ = P₁ * T₂ / T₁
Substituting the known values:
P₂ = (1.00*10^3 kPa) * (323.15 K) / (293.15 K)
Calculating this expression will give us the new pressure, P₂.
(P1/V1) = (P2/T2)
T must be in kelvin.