During an isovolumetric process, the pressure on the gas is doubled and the amount of gas is tripled. If the initial temperature of the gas is 300k, what is thefinal temperture.
To determine the final temperature of the gas during an isovolumetric process, we can make use of the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume (constant in this case since it's an isovolumetric process)
n = number of moles of gas
R = ideal gas constant
T = temperature
Now let's consider the initial and final states of the gas in this problem. The initial and final pressures and amounts of gas are given as follows:
Initial pressure (P1) = P
Final pressure (P2) = 2P (since it is doubled)
Initial amount of gas (n1) = n
Final amount of gas (n2) = 3n (since it is tripled)
Initial temperature (T1) = 300 K
Since the volume (V) remains constant, the equation PV = nRT can be simplified to:
P1T1 = P2T2
Rearranging the equation to solve for the final temperature (T2):
T2 = (P1T1) / P2
Substituting the given values:
T2 = (P * 300 K) / (2P)
Simplifying the equation:
T2 = 150 K
Therefore, the final temperature (T2) is 150 K.