The gas inside of a container exerts #8 Pa# of pressure and is at a temperature of #45 ^o K#. If the temperature of the gas changes to #80 ^oK#, what is the new pressure of the gas?

Question

The gas inside of a container exerts #8   Pa# of pressure and is at a temperature of #45 ^o K#.  If the temperature of the gas changes to #80 ^oK#, what is the new pressure of the gas?

Amelia Adams · Accepted Answer

With a constant container volume, Charles' Law becomes simply:
#P_1/T_1 = P_2/T_2#
Rearrange for your known values:
#P_2 = P_1 * T_2/T_1# The ideal gas laws (Charles' Law) state: #(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2# Where #P_1,_2# are pressures – units don't matter in this case as long as they are consistent, because this is a ratio. #V_1,_2# are the corresponding volumes in Liters #T_1,_2# are the temperatures in degrees Kelvin

Axel Acevedo · Answer

undefined To find the new pressure of the gas, we can use the combined gas law equation:

P1/T1 = P2/T2

Where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure
T2 = final temperature

Given:
P1 = 8 Pa
T1 = 45 K
T2 = 80 K

Substitute the values into the equation:

8 Pa / 45 K = P2 / 80 K

Solve for P2:

P2 = (8 Pa * 80 K) / 45 K
P2 ≈ 14.22 Pa

Therefore, the new pressure of the gas is approximately 14.22 Pa.