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A sealed gas cylinder on the back of an open truck experiences a temperature change from -21.1 ËšC to 36.6 ËšC as it is driven from North Dakota to Arizona. If the pressure gauge on the tank reads 134.8 atm in North Dakota, what will the gauge read in Arizona, in atm?

Answer :

The pressure gauge on the gas cylinder in Arizona will read approximately 165.97 atm.

To calculate the new pressure reading in Arizona, we can use the ideal gas law equation: P₁V₁/T₁ = P₂V₂/T₂

where:

P₁ and P₂ are the initial and final pressures,

V₁ and V₂ are the initial and final volumes (assuming the volume remains constant),

T₁ and T₂ are the initial and final temperatures.

Given:

Initial temperature (T₁) = -21.1 ˚C = 251.05 K (converted to Kelvin)

Final temperature (Tâ‚‚) = 36.6 ËšC = 309.75 K (converted to Kelvin)

Initial pressure (P₁) = 134.8 atm

Final pressure (Pâ‚‚) = ?

Assuming the volume remains constant, V₁ = V₂

Using the ideal gas law equation:

P₁V₁/T₁ = P₂V₂/T₂

Since V₁ = V₂, we can simplify the equation to:

P₁/T₁ = P₂/T₂

Now we can substitute the known values and solve for Pâ‚‚:

P₂ = (P₁ x T₂) / T₁

Pâ‚‚ = (134.8 atm x 309.75 K) / 251.05 K

Calculating the value:

Pâ‚‚ = 165.97 atm (rounded to two decimal places)

Therefore, the pressure gauge on the gas cylinder in Arizona will read approximately 165.97 atm.

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