Answer
See the detailed answer below.
Work Step by Step
a) The volume has tripled, so the final volume is
$$V_2=3V_1\tag 1$$
And since the gas undergoes an isobaric process, $P_1=P_2$;
$$\dfrac{\color{red}{\bf\not} P_1V_1}{T_1}=\dfrac{\color{red}{\bf\not} P_2V_2}{T_2}$$
Hence,
$$T_2=\dfrac{V_2T_1}{V_1}=\dfrac{(3\color{red}{\bf\not} V_1)T_1}{\color{red}{\bf\not} V_1}$$
Thus,
$$T_2=3T_1=3(20+273)$$
$$T_2=\bf 879\;\rm K=\color{red}{606^\circ}C$$
Now we need to find the initial pressure which is given by
$$P_1V_1=nRT_1$$
Hence,
$$V_1=\dfrac{nRT_1}{P_1}\tag 2$$
where $$n=\dfrac{m}{M_{N_2}}=\dfrac{m}{2M_N}$$
Plugging the known
$$n=\dfrac{5}{2(14)}=\bf \frac{5}{28}\;\rm mol$$
Hence,
$$V_1=\dfrac{nRT_1}{P_1}=\dfrac{(\frac{5}{28})(8.31)(20+273)}{(3\times 1.013\times 10^5)}$$
$$V_1=\bf 1.4307\times 10^{-3}\;\rm m^3\approx \bf 1431\;cm^3$$
Therefore,
$$V_2=3\times1.4307\times 10^{-3} $$
$$V_2=\color{red}{\bf 4.292\times 10^{-3}}\;\rm m^3\approx \bf 4293\;cm^3$$
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b) Since it is an isobaric process, then the heat transferred is given by
$$Q=nC_{\rm p}\Delta T$$
Plugging the known;
$$Q=\frac{5}{28} (29.1) (606-20)$$
$$Q=\color{red}{\bf3.045\times 10^3}\;\rm J$$
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c) Now the gas undergoes an isochoric process, so
$$\dfrac{P_2\color{red}{\bf\not} V_2}{T_2}=\dfrac{P_3\color{red}{\bf\not} V_3}{T_3}$$
where $T_3=T_1$ and $P_2=P_1$
$$\dfrac{P_1 }{T_2}=\dfrac{P_3 }{T_1}$$
Thus,
$$P_3=\dfrac{P_1T_1}{T_2}$$
Plugging the known;
$$P_3=\dfrac{(3)(20+273)}{(606+273)}$$
$$P_3=\color{red}{\bf1.0}\;\rm atm$$
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d)
Since it is an isochoric process, then the heat transferred out from the gas is given by
$$Q=nC_{\rm v}\Delta T$$
Plugging the known;
$$Q=\frac{5}{28} (20.8) (20-606)$$
$$Q=\color{red}{\bf-2.176\times 10^3}\;\rm J$$
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e) We have two processes:
$\bullet$1- An isobaric expansion process.
It starts at $(V_1,P_1)=(1431\;\rm cm^3,3\;atm)$ and ends at $(V_2,P_3)=(4293\;\rm cm^3,3\;atm)$
$\bullet$ 2- An isochoric compression process.
It starts at $(V_2,P_3)=(4293\;\rm cm^3,3\;atm)$ and ends at
$(V_3,P_3)=(4293\;\rm cm^3,1\;atm)$
See the graph below.
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