If the temperature of a gas confined to such a cylinder is raised from 293°C to 674°C, what is the ratio of the initial volume to the final volume if the pressure exerted on the gas remains constant?

Answer 1

You don't describe the cylinder, but I have to guess, based on the verbiage in the question, that this is some sort of a flexible wall cylinder, perhaps something with a piston-type configuration that allows it to grow as needed to keep the pressure constant.

The Ideal Gas law say PV = nRT or PV/T = nR

If we have a confined condition (no gas comes in or leaves), then we can say that "nR" never changes meaning that P₁V₁/T₁ = P₂V₂/T₂ and, if we know that P₁ and P₂ are equal then:

V₁/T₁ = V₂/T₂ or V₁/V₂ = T₁/T₂

But we MUST use Kelvin as the unit of temperature so T₁ = 293 + 273.15 = 566.15 K and T₂ = 674 + 273.15 = 947.15 K therefore:

V₁/V₂ = 566.15/947.15 = 0.598