A cylinder has a piston at one end that can be moved in or out to change the vol

Question

A cylinder has a piston at one end that can be moved in or out to change the volume of gas inside. The other end is fitted with a valve. Initially the cylinder contains3.05-mol of an ideal gas. The piston is now pushed in to decrease the volume of gas to three-fifths its initial value without causing any change in temperature. In order to keep the pressure constant as well, how many moles of gas need to be released through the valve? The temperature of a gas increase from 31.5 k to 73.5 K while its volume remains constant. What is the new pressure? Give your answer as a multiple of the initial pressure P_1

Explanation / Answer

V/n = RT/P = constant

hence Vi/ni = Vf/nf

Vi = initial volume

Vf = final Volume = 3Vi/5 = 0.6 Vi

Vi/3.05 = (0.6 Vi)/nf

nf = 1.83 moles

number of moles released = ni - nf = 3.05 - 1.83 = 1.22

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