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The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point A (pressure PA, volume = VA) and expands isothermally at temperature T until point B (pressure = PB, volume VB) is reached. During this expansion, the input heat of magnitude Qn enters the gas from the hot reservoir of the engine. Then, from point B to point C (pressure Pc.volume Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature T, from point C to point D (pressure = PD, volume = VD). During this compression, heat of magnitude Qe is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point D to point A, where the gas is back in its initial state. The overall process A to B to C to D to A is called a Carnot cycle. Prove for this cycle that loed - Te The work done during the cycle equals the area enclosed by the path on the PV diagram. Weng -Te Th V | Obtain the relationship lcl_ Tc IQH| TH Hint: Use the expressions in items #1 and #3 and the relationship for the adiabatic expressions PgV = PcV% and PAV = PpV. %3D %3!

The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point A (pressure PA, volume = VA) and expands isothermally at temperature T until point B (pressure = PB, volume VB) is reached. During this expansion, the input heat of magnitude Qn enters the gas from the hot reservoir of the engine. Then, from point B to point C (pressure Pc.volume Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature T, from point C to point D (pressure = PD, volume = VD). During this compression, heat of magnitude Qe is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point D to point A, where the gas is back in its initial state. The overall process A to B to C to D to A is called a Carnot cycle. Prove for this cycle that loed - Te The work done during the cycle equals the area enclosed by the path on the PV diagram. Weng -Te Th V | Obtain the relationship lcl_ Tc IQH| TH Hint: Use the expressions in items #1 and #3 and the relationship for the adiabatic expressions PgV = PcV% and PAV = PpV. %3D %3!

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem: The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point A (pressure = PA, volume = VA) and expands isothermally at temperature T until point B (pressure = PB, volume = V B) is reached. During this expansion, the input heat of magnitude Qn enters the gas from the hot reservoir of the engine. Then, from point B to point C (pressure Pc. volume = Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature T. from point C to point D (pressure = PD, volume = VD). During this compression, heat of magnitude Q. is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point D to point A, where the gas is back in its initial state. The overall process A to B to C to D to A is called a Carnot cycle. Prove The work done during the cycle equals the area enclosed by the path on the PV diagram. B Weng T C -Te for this cycle that Od Te Ienl Th V Obtain the relationship IQcl _Tc TH Hint: Use the expressions in items #1 and # 3 and the relationship for the adiabatic expressions PgV = PcVě and PAV = PpV. %3D
Transcribed Image Text:Problem: The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point A (pressure = PA, volume = VA) and expands isothermally at temperature T until point B (pressure = PB, volume = V B) is reached. During this expansion, the input heat of magnitude Qn enters the gas from the hot reservoir of the engine. Then, from point B to point C (pressure Pc. volume = Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature T. from point C to point D (pressure = PD, volume = VD). During this compression, heat of magnitude Q. is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point D to point A, where the gas is back in its initial state. The overall process A to B to C to D to A is called a Carnot cycle. Prove The work done during the cycle equals the area enclosed by the path on the PV diagram. B Weng T C -Te for this cycle that Od Te Ienl Th V Obtain the relationship IQcl _Tc TH Hint: Use the expressions in items #1 and # 3 and the relationship for the adiabatic expressions PgV = PcVě and PAV = PpV. %3D
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