A helium balloon has a volume of 18.1 L
when the pressure is 1.045 atm and the tem�perature is 19 ◦C. The balloon is cooled at
a constant pressure until the temperature is
−16◦C. What is the volume of the balloon at
this stage?
Answer in units of L.
To find the volume of the balloon at -16°C, we can use the combined gas law formula:
(P1 * V1) / T1 = (P2 * V2) / T2
Given:
P1 = 1.045 atm (initial pressure)
V1 = 18.1 L (initial volume)
T1 = 19°C + 273.15 = 292.15 K (initial temperature in Kelvin)
P2 = 1.045 atm (constant pressure)
T2 = -16°C + 273.15 = 257.15 K (final temperature in Kelvin)
Substituting the values into the formula, we get:
(1.045 * 18.1) / 292.15 = (1.045 * V2) / 257.15
Solving for V2 (volume at -16°C):
V2 = (1.045 * 18.1 * 257.15) / (1.045 * 292.15)
V2 = (470.47225) / (303.648175)
V2 ≈ 1.548 L
Therefore, the volume of the balloon at -16°C is approximately 1.548 L.
To determine the volume of the balloon at -16°C, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
- P1 and P2 are the initial and final pressures, respectively.
- V1 and V2 are the initial and final volumes of the balloon, respectively.
- T1 and T2 are the initial and final temperatures, respectively.
Given:
P1 = 1.045 atm
V1 = 18.1 L
T1 = 19°C = 19 + 273.15 K (convert to Kelvin)
We need to determine V2 when T2 = -16°C.
Step 1: Convert the temperatures to Kelvin:
T1 = 19 + 273.15 = 292.15 K
T2 = -16 + 273.15 = 257.15 K
Step 2: Plug the values into the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
(1.045 atm * 18.1 L) / (292.15 K) = (P2 * V2) / (257.15 K)
Step 3: Isolate V2:
(1.045 atm * 18.1 L * 257.15 K) / (292.15 K) = P2 * V2
V2 = (1.045 atm * 18.1 L * 257.15 K) / (292.15 K * P2)
Step 4: Substitute P2:
Since the temperature is cooled at a constant pressure, P1 = P2.
V2 = (1.045 atm * 18.1 L * 257.15 K) / (292.15 K * 1.045 atm)
V2 = (18.1 L * 257.15 K) / 292.15 K
Step 5: Calculate V2:
V2 = 15.94 L
Therefore, the volume of the balloon at -16°C is 15.94 L.
PV=kT
since P is also constant,
V/T is constant. So you need
V/(273-16) = 1.045/(273+19)