Question

B. The PV diagram below shows several different ideal gas processes. A ? C is isothermal process. p? = 3.10 x 10? Pa, p? = 1.55 x 10? Pa, V? = 2.35 x 10?³ m³. a) What are the processes A?B, B?C, A?D, D?C? b) What is V?? (V? = 4.70 x 10?³ m³) c) How much work does the gas do as it goes along the path A?B?C? How much work does the gas do as it goes along the path A?D?C? d) If as the gas goes on the path A?B?C, 1000 J of heat are added to the gas. How much heat is added to the gas as it goes along the path A?D?C? e) If considering the PV diagram ABCDA as a heat engine, what is total work done by the gas in the cyclical process ABCDA? f) If 1000 J of heat are added to the gas during each one cycle, what is the efficiency of this heat engine?

          B. The PV diagram below shows several different ideal gas processes. A ? C is isothermal process. p? = 3.10 x 10? Pa, p? = 1.55 x 10? Pa, V? = 2.35 x 10?³ m³.

a) What are the processes A?B, B?C, A?D, D?C?
b) What is V?? (V? = 4.70 x 10?³ m³)
c) How much work does the gas do as it goes along the path A?B?C? How much work does the gas do as it goes along the path A?D?C?
d) If as the gas goes on the path A?B?C, 1000 J of heat are added to the gas. How much heat is added to the gas as it goes along the path A?D?C?
e) If considering the PV diagram ABCDA as a heat engine, what is total work done by the gas in the cyclical process ABCDA?
f) If 1000 J of heat are added to the gas during each one cycle, what is the efficiency of this heat engine?

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B. The PV diagram below shows several different ideal gas processes. A ? C is isothermal process. p? = 3.10 x 10? Pa, p? = 1.55 x 10? Pa, V? = 2.35 x 10?³ m³.

a) What are the processes A?B, B?C, A?D, D?C?
b) What is V?? (V? = 4.70 x 10?³ m³)
c) How much work does the gas do as it goes along the path A?B?C? How much work does the gas do as it goes along the path A?D?C?
d) If as the gas goes on the path A?B?C, 1000 J of heat are added to the gas. How much heat is added to the gas as it goes along the path A?D?C?
e) If considering the PV diagram ABCDA as a heat engine, what is total work done by the gas in the cyclical process ABCDA?
f) If 1000 J of heat are added to the gas during each one cycle, what is the efficiency of this heat engine?

Added by Laura S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Adi S

06/06/2022

Step 1

- Process A to B: Since the pressure increases while the volume remains constant, this is an isochoric (or isovolumetric) process. - Process B to C: Given in the question, this is an isothermal process, where the temperature remains constant. - Process A to C: Show more…

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B. The PV diagram below shows several different ideal gas processes. A → C is isothermal process. p₁ = 3.10 x 10⁵ Pa, p₂ = 1.55 x 10⁵ Pa, V₁ = 2.35 x 10⁻³ m³. a) What are the processes A→B, B→C, A→D, D→C? b) What is V₂? (V₂ = 4.70 x 10⁻³ m³) c) How much work does the gas do as it goes along the path A→B→C? How much work does the gas do as it goes along the path A→D→C? d) If as the gas goes on the path A→B→C, 1000 J of heat are added to the gas. How much heat is added to the gas as it goes along the path A→D→C? e) If considering the PV diagram ABCDA as a heat engine, what is total work done by the gas in the cyclical process ABCDA? f) If 1000 J of heat are added to the gas during each one cycle, what is the efficiency of this heat engine?

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Transcript

00:01 In the question they have given us a pv graph and they have given us a value p1 is equal to 3 .10 into 10 power 5 pascal and p2 they have given us 1 .55 into 10 power 5 pascal and v1 they have given us 2 .35 into 10 power 5 pascals and the 1 1 they have given us 2 .35 into 10 power minus 3 meter cube.

00:29 And the first question that they are asked is what is the process ab, b, c, ad and d .a.

00:36 So the process a .b.

00:39 And the process d .c.

00:43 Are both isobaric as there is no change in pressure.

00:53 The process a .d.

00:59 And b .c.

01:03 Are both iso -coric as there is no change in volume.

01:10 So this is the both of the process.

01:15 Now coming to question b, what is the volume v1? they're asking v1.

01:21 So from the graph, it is evident that pressure and volume have a inverse relation.

01:25 So p1 by p2 equals v2 by v1.

01:29 So substitute the values 3 .10 into 10 power 5 divided by 1 .55 into 10 power 5 equals v2 we don't.

01:42 Know divided by v1 is 2 .35 into 10 power minus 3 meter cube so this will give us the answer v2 as 4 .70 into 10 to the power of minus 3 meter cube so this is the volume of the second v2 now finding out they're asking me the third question what is the work done along the path a -b -c and adc.

02:12 The workdown along path a -b -c is a combination of a -b plus b -c.

02:18 If you notice the graph, we'll get to know that the work -down along b -c is 0 as there is no change in volume.

02:27 So the work -down will be only along a -b which is b1 into v2 minus v1.

02:35 Now if you substitute the values 3 .10 into 10 power 5...

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