Simple question about Nitrogen

If I fill a cylinder with 2 atmospheres of Nitrogen at 70-75 degrees f, then gradually lower the temperature to 35-40F will there be a resultant change in the pressure/volume of Nitrogen inside of the cylinder?
If so, will the opposite be true when returning to normal temperature?
:?:

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PV=nRT right?

where (nR) will just say is constant for your thought experiment. Since its in a sealed cylinder the Volume (V) is constant as well, so it simplfies to:

P=T

so if T decreases, so does P

If T increases, so does P

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