91Ó°ÊÓ

a.

- $4→3$This is a volume-increasing isobaric process (isobaric expansion). The effort done is good since the gas expands.

Also, in the isobaric process, the temperature rises, implying that the thermal energy rises.

According to the first law of thermodynamics, the received heat is positive because both the work done and the change in thermal energy are positive$\mathrm{Q}=\mathrm{W}+{\mathrm{Δ·¡}}_{\mathrm{th}}$.

In this process, the heat is transferred to the gas.

b.

The heat removed from the cold reservoir is${\mathrm{Q}}_{\mathrm{C}}$.

The gas takes heat only when it reaches its lowest temperature of $300\mathrm{K}$at point four (the temperature of the cold reservoir).

And it begins to release heat when it reaches its greatest temperature of $2700\mathrm{K}$at point two (the temperature of the hot reservoir) (the temperature of the hot reservoir).

c.

Heat is,

${\mathrm{Q}}_{\mathrm{C}}={\mathrm{Q}}_{43}+{\mathrm{Q}}_{32},$

${\mathrm{Q}}_{\mathrm{H}}=\left|{\mathrm{Q}}_{21}\right|+\left|{\mathrm{Q}}_{14}\right|$

So,

localid="1650295407041" ${\mathrm{Q}}_{43}=7.09×{10}^5\mathrm{J},$

localid="1650295443209" ${\mathrm{Q}}_{32}=15.19×{10}^5\mathrm{J},$

${\mathrm{Q}}_{21}=-21.27×{10}^5\mathrm{J},$

localid="1650295457797" ${\mathrm{Q}}_{14}=-5.06×{10}^5\mathrm{J}.$

This yields

localid="1650295473714" ${\mathrm{Q}}_{\mathrm{C}}=22.28×{10}^5\mathrm{J},$and${\mathrm{Q}}_{\mathrm{H}}=26.33×{10}^5\mathrm{J}$

d.

We take heat from the cold reservoir and transfer it to the hot reservoir in larger amounts.

This is impossible without putting in effort, according to the second rule of thermodynamics, hence this area is${\mathrm{W}}_{\mathrm{in}}$.

Another criterion is that if a cycle is clockwise (cw), the area is${\mathrm{W}}_{\mathrm{out}}$, and if it is counterclockwise (ccw), the area is ${\mathrm{W}}_{\mathrm{in}}$.

The cycle in our situation is counterclockwise.

e.

This cycle isn't modelled after a refrigerator.

Because there is no colder reservoir than${\mathrm{T}}_{\mathrm{C}}$ with which the gas can exchange heat.

The gas must reach lower temperatures than ${\mathrm{T}}_{\mathrm{C}}=300\mathrm{K}$, which is only possible via adiabatic expansion (no heat transfer).