Question

A gas is heated from 246 K to 289 K while its volume is increased from 22.0 L to 30.5 L by moving a large piston within a cylinder. If the original pressure was 0.98 atm, what would be the final pressure?

Answer 1

The answer is 0.998 atm.

To determine the final pressure of the gas, 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 (what we want to find)
V2 = final volume
T2 = final temperature

Given:
P1 = 0.98 atm
V1 = 22.0 L
T1 = 246 K
V2 = 30.5 L
T2 = 289 K

Plugging in the values into the equation, we have:

0.98 atm * 22.0 L / 246 K = P2 * 30.5 L / 289 K

Now we can solve for P2:

P2 = (0.98 atm * 22.0 L * 289 K) / (246 K * 30.5 L)
P2 = 0.98 * 22.0 * 289 / (246 * 30.5)
P2 ≈ 0.998 atm

Therefore, the final pressure of the gas would be approximately 0.998 atm.