Question

3. One kilogram of air as an ideal gas executes a Carnot power cycle having a thermal efficiency of 60%. The heat transfer to the air during the isothermal expansion is 40 kJ. At the end of the isothermal expansion, the pressure is 5.6 bar and the volume is 0.3 $m^3$. Determine (a) the maximum and minimum temperatures for the cycle, in K. (b) the pressure and volume at the beginning of the isothermal expansion in bar and $m^3$, respectively. (c) the work and heat transfer for each of the four processes, in kJ. (d) Sketch the cycle on $p-v$ coordinates.

          3. One kilogram of air as an ideal gas executes a Carnot power cycle having a thermal efficiency
of 60%. The heat transfer to the air during the isothermal expansion is 40 kJ. At the end
of the isothermal expansion, the pressure is 5.6 bar and the volume is 0.3 $m^3$. Determine
(a) the maximum and minimum temperatures for the cycle, in K.
(b) the pressure and volume at the beginning of the isothermal expansion in bar and $m^3$,
respectively.
(c) the work and heat transfer for each of the four processes, in kJ.
(d) Sketch the cycle on $p-v$ coordinates.

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3. One kilogram of air as an ideal gas executes a Carnot power cycle having a thermal efficiency
of 60%. The heat transfer to the air during the isothermal expansion is 40 kJ. At the end
of the isothermal expansion, the pressure is 5.6 bar and the volume is 0.3 m^3. Determine
(a) the maximum and minimum temperatures for the cycle, in K.
(b) the pressure and volume at the beginning of the isothermal expansion in bar and m^3,
respectively.
(c) the work and heat transfer for each of the four processes, in kJ.
(d) Sketch the cycle on p-v coordinates.

Added by Keith O.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

06/15/2022

Step 1

We can use the ideal gas law, which states that for an isothermal process, the product of pressure and volume is constant. This can be expressed as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Show more…

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Could you explain the question with the reasons of the actions we take. Thanks. of 60%. The heat transfer to the air during the isothermal expansion is 40 kJ. At the end of the isothermal expansion,the pressure is 5.6 bar and the volume is 0.3m3.Determine a the maximum and minimum temperatures for the cycle, in K. (b) the pressure and volume at the beginning of the isothermal expansion in bar and m respectively. c the work and heat transfer for each of the four processes, in kJ. (d) Sketch the cycle on p-v coordinates

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Transcript

00:02 The thermal efficiency, n, is equal to 1 minus t cold or divided by t hot.

00:08 So our n is 1 minus 300 divided by 750, which is 60%.

00:15 So that's our thermal efficiency of our cycle.

00:18 We'd like to find the work and heat transfer.

00:22 So our volume, we can calculate the volume at the beginning of our isothermal expansion process.

00:32 Q12 is equal to mr -th ln of v2 over v1.

00:39 So if we plug in, we have ln 0 .4 over v1 is equal to 60 divided by 2 times 0 .287 times 750.

00:50 So v1 is 0 .347 meters cubed.

00:56 So that's the volume at the beginning of our process.

00:59 P2, we can determine the pressure using the ideal gas model.

01:05 P2 is mrt2 divided by v2.

01:11 So p2 is 1076 .2 kpa.

01:17 Now the pressure at the beginning of the process, we use p1v1 is equal to p2v2.

01:23 So plugging in, p1 is equal to 1237 .3 kpa.

01:34 Now, let's calculate the work and heat transfer.

01:39 So we know delta u12 is equal to q minus work.

01:46 And but delta u is just mcv t2 minus t1 is equal to q minus work.

01:53 But since t1 is equal to t2, we find work 12 equal to 60 kilojoules...

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