To what temperature must a mass of Nitrogen at 0°c,be heated so that both its volume and pressure will be doubled?
To find the temperature to which a mass of Nitrogen at 0°C must be heated in order for both its volume and pressure to double, we can make use of the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P is the pressure,
V is the volume,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature in Kelvin.
To simplify the equation, we will assume that the number of moles of Nitrogen remains constant. Therefore, we can rewrite the equation as:
P1V1/T1 = P2V2/T2
Where the subscripts 1 and 2 refer to the initial and final states respectively.
Given:
P1 = Initial pressure of Nitrogen
V1 = Initial volume of Nitrogen
T1 = Initial temperature of Nitrogen (0°C = 273.15 K)
P2 = Final pressure (doubled)
V2 = Final volume (doubled)
T2 = Final temperature (what we need to find)
To solve for T2, we rearrange the equation:
T2 = (P2V2 * T1) / (P1V1)
Substituting the given values:
P1 = Initial pressure = P2 = 1 (since it doubles)
V1 = Initial volume = V2 = 1 (since it doubles)
T1 = 0°C = 273.15 K
Plugging the values into the equation:
T2 = (1 * 1 * 273.15) / (1 * 1)
T2 = 273.15 K
Therefore, the Nitrogen must be heated to a temperature of 273.15 Kelvin (which is equivalent to 0°C) in order for both its volume and pressure to double.
since PV = kT
(2P)(2V) = 4PV = k(4T)
so, 4 times the (Kelvin) temperature