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A steel tank of nitrogen gas is left in the sun. Initially, the gas's pressure is 150 atm at 27 degrees Celsius. The tank heats up to 55 degrees Celsius after several hours in the sun. What is the new pressure of the gas in the tank?

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quasarJose

Answer:

164atm

Explanation:

Given parameters:

Initial pressure of tank = 150atm

Initial temperature of tank  = 27°C  = 27 + 273 = 300K

New temperature of tank  = 55°C  = 328K

Unknown:

New pressure of gas  = ?

Solution:

From the combined gas law, at constant volume, the pressure of a given gas varies directly with the absolute temperature.

 Mathematically;

       [tex]\frac{P_{1} }{T_{1} }[/tex]   = [tex]\frac{P_{2} }{T_{2} }[/tex]  

P and T are pressure and temperature values

1 and 2 are the initial and new states

  Insert the parameters and solve;

   [tex]\frac{150}{300}[/tex]   = [tex]\frac{P_{2} }{328}[/tex]  

     300P₂  = 150 x 328

           P₂  = 164atm

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