Answer :
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of temperature, pressure, and volume of a gas.the pressure gauge on the gas cylinder will read approximately 185.3 atm in Arizona.
The combined gas law equation is given by:
(P1 * V1) / T1 = (P2 * V2) / T2
Given:
P1 = 138.8 atm (pressure in North Dakota)
T1 = -20.5 °C = -20.5 + 273.15 K (temperature in North Dakota)
T2 = 39.3 °C = 39.3 + 273.15 K (temperature in Arizona)
V1 and V2 are the volumes of the gas cylinder, which we assume to remain constant.
Substituting the values into the equation, we have:
(138.8 * V1) / (-20.5 + 273.15) = (P2 * V2) / (39.3 + 273.15)
Since the volume is constant, V1/V2 cancels out, and we can solve for P2:
P2 = (138.8 * (39.3 + 273.15)) / (-20.5 + 273.15)
Calculating the expression, we find:
P2 ≈ 185.3 atm
Therefore, the pressure gauge on the gas cylinder will read approximately 185.3 atm in Arizona.
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