Answer
See the detailed answer below.
Work Step by Step
First, we need to find the number of moles in 5 g nitrogen.
$$n=\dfrac{m_{N_2}}{M_{N_2}}=\dfrac{m_{N_2}}{2M_N}$$
Plugging the known;
$$n =\dfrac{5}{2(14)}=\bf\frac{5}{28}\;\rm mol$$
Now we need to find the initial volume by using the ideal gas law of
$$P_1 V_1=nRT_1$$
Hence,
$$V_1=\dfrac{nRT_1}{P_1 }$$
Plugging the known;
$$V_1=\dfrac{(\frac{5}{28})(8.31)(20+273)}{3\times 1.013\times 10^5}$$
$$V_1=\bf 1.431\times 10^{-3}\;\rm m^3=\bf 1431\;\rm cm^3$$
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a) We need to find the volume at the end of the isobaric process.
We know that the volume has tripled. So,
$$V_2=3V_1=3\times1431$$
$$V_2=\color{red}{\bf 4293}\;\rm cm^3$$
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b) The temperature after the expansion is the temperature at the end of the isobaric process which is given by
$$P_2V_2= nRT_2 $$
Hence,
$$T_2=\dfrac{P_2V_2}{nR}$$
where $P_1=P_2=3\;\rm atm$, and $V_2=3V_1$
$$T_2=\dfrac{3P_1V_1}{nR}$$
And to find it in Celsius,
$$T_2=\dfrac{3P_1V_1}{nR}-273$$
Plugging the known
$$T_2=\dfrac{3 (3\times 1.013\times 10^5)(1431\times 10^{-6})}{(\frac{5}{28})(8.31)}-273$$
$$T_2=\color{red}{\bf 606}^\circ \rm C$$
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c) Now the gas undergoes an isochoric process and at the end of this process, $T_3=T_1$
Hence, the pressure is given by
$$P_3 =\dfrac{nRT_3}{V_3}$$
where $V_3=V_2=3V_1$, and $T_3=T_1$.
$$P_3 =\dfrac{nRT_1}{V_2}$$
Plugging the known;
$$P_3 =\dfrac{(\frac{5}{28})(8.31)(20+273)}{3\times 1431\times 10^{-6}}$$
$$P_3=1.013\times 10^5=\color{red}{\bf 1}\;\rm atm$$
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c) Now the gas undergoes an isothermal process and at the end of this process, $V_4=V_1$
Hence, the pressure is given by
$$P_4 =\dfrac{nRT_4}{V_4}$$
where $V_4=V_1$, and $T_4=T_3=T_1$.
$$P_4 =\dfrac{nRT_1}{V_1}$$
Plugging the known;
$$P_3 =\dfrac{(\frac{5}{28})(8.31)(20+273)}{ 1431\times 10^{-6}}$$
$$P_3=3.034\times 10^5=\color{red}{\bf 3}\;\rm atm$$
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d) We have here 4 points:
$\bullet$ $ (V_1,P_1)=\rm(1431\;cm^3,3\;atm)$
$\bullet$ $ (V_2,P_2)=\rm(4293\;cm^3,3\;atm)$
$\bullet$ $ (V_3,P_3)=\rm(4293\;cm^3,1\;atm)$
$\bullet$ $ (V_4,P_4)=\rm(1431\;cm^3,3\;atm)$
We can see that the 4th point is actually the 1st point. So it ends where it starts.
See the graph below.
