A certain volume of a gas at 298k is heated such that its volume and pressure are now four times thier original value. What is the new temperature?
If PV increases by 16, T has increased by 4.
4(298) is really hot.
oops, T has increased by 16. THat is even hotter.
1788
To determine the new temperature of the gas after it is heated, we can use the combined gas law equation:
(P1 × V1) / T1 = (P2 × V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
Let's assign variables to the given values:
P1 = initial pressure = unknown
V1 = initial volume = unknown
T1 = initial temperature = 298 K
P2 = final pressure = 4 times the initial pressure = 4P1
V2 = final volume = 4 times the initial volume = 4V1
T2 = final temperature = unknown
Substituting the given values into the combined gas law equation:
(P1 × V1) / T1 = (P2 × V2) / T2
(unknown × unknown) / 298 = (4P1 × 4V1) / T2
Simplifying the equation:
(unknown^2) / 298 = (16P1V1) / T2
We can solve this equation by using the given information, which states that the final volume and pressure are four times their original values:
(unknown^2) / 298 = (16 × unknown × unknown) / T2
Now we can simplify:
unknown^2 = (16 × unknown × unknown × T2) / 298
Cross-multiplying:
unknown^2 × 298 = 16 × unknown × unknown × T2
We can further simplify by dividing both sides by unknown × unknown:
298 = 16 × T2
Now we can isolate T2 by dividing both sides by 16:
T2 = 298 / 16
T2 ≈ 18.625
Therefore, the new temperature of the gas is approximately 18.625 K.