To solve this problem, we can use the combined gas law, which incorporates the relationship between pressure, volume, and temperature of a gas.
The combined gas law is given by:
(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
Given values: P1 = 136 ATM V1 = (since the cylinder is rigid, the volume remains constant) T1 = 25°C = 25 + 273.15 = 298.15 K T2 = 0°C = 0 + 273.15 = 273.15 K
Since the volume is constant, we can simplify the equation to:
P1 / T1 = P2 / T2
Plugging in the values, we have:
136 ATM / 298.15 K = P2 / 273.15 K
To find P2, we rearrange the equation:
P2 = (136 ATM × 273.15 K) / 298.15 K
Simplifying the equation, we get:
P2 ≈ 124.58 ATM
Therefore, the gas pressure in the cylinder when it is placed in iced water at 0.0 degrees Celsius is approximately 124.58 ATM.