You take a gas at T = 27 degs C in a box and compress it at constant pressure (a

Question

You take a gas at T = 27 degs C in a box and compress it at constant pressure (atmospheric pressure) from a volume of 0.100 m^3 down to 0.055 m^3. You then let the gas expand at a constant temperature back to a volume of 0.100 m^3. Finally, you hold the walls of the box fixed so the volume stays fixed and let the gas return to its initial state. a. How many moles of the gas are there? b. What is the temperature after the initial compression? c. What is pressure after you let the gas volume expand back to 0.100 m^3? d. What is the final temperature of the gas upon completing the closed cycle? e. How much work (W) was done during each step of the cycle? Label the steps according to their type (i.e. isothermal, isobaric, isochoric). f. Find the change in internal energy (delta U) during each step. g. Calculate the heat flowing into the gas during each step (Q). h. Draw all three of the steps on a single P-V diagram. Show appropriate labels and include a depiction of the TOTAL work done on the gas.

Explanation / Answer

part a:

initial temperature=T=27 degrees=273+27=300 K

initial pressure=1 atm=101325 N/m^2

initial volume=0.1 m^3

then number of moles=pressure*volume/(gas constant*temperature)

=4.0624

part b:

as the initial compression is done at constant pressure, volume/temperature remains constant

let temperature after compression is T

then 0.1/300=0.055/T

==>T=165 K

=-108 degree celcius

part c:

in the expansion process, as temperature is constant

pressure*volume will remain constant

if pressure at the end of expansion is P

then 101325*0.055=P*0.1

==>P=55728.75 N/m^2

part d:

in the final process , volume remains fixed.

hence pressure/temperature remains constant

==>55728.75/165=101325/T

==>T=300 K=27 degree celcius

hence final temperature is 27 degree celcius.

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