A gas is in a closed container of volume 35 cm³.If its temperature is initially 278 K,by how much do you need to change the temperature in order to increase its pressure from the initial 1 atm to 1.2 atm?

Question

Quizplus · Accepted Answer

For a gas in a closed container, the relationship between pressure and temperature is given by Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. Mathematically, this can be expressed as P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature, respectively.Given:- Initial pressure (P1) = 1 atm- Final pressure (P2) = 1.2 atm- Initial temperature (T1) = 278 KWe need to find the final temperature (T2) that would result in the pressure increasing to 1.2 atm. Rearranging the equation for T2 gives us T2 = (P2/P1) * T1.Plugging in the given values:T2 = (1.2/1) * 278 = 1.2 * 278 = 333.6 KThe change in temperature (ΔT) required is the difference between the final and initial temperatures:ΔT = T2 - T1 = 333.6 K - 278 K = 55.6 KSince the question asks for how much the temperature needs to change and the options are given in whole numbers, the closest option to 55.6 K is +56 K.

A Gas Is in a Closed Container of Volume 35