Diesel Cycle - Revision history

Mol: /* Diesel Cycle and Ideal Gas */

2026-03-30T18:36:15Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:36, 30 March 2026
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	For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.		For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.

	For the '''Isochoric process''' <math>\Delta V=0</math>, and thus we have <math>dU ~~= dQ~~ = mc_v dT</math> which gives <math>\Delta Q = m c_v\Delta T</math>.		For the '''Isochoric process''' <math>\Delta V=0</math>, and thus we have <math>dQ = dU = mc_v dT</math> which gives <math>\Delta Q = m c_v\Delta T</math>.

	<math>		<math>

2026-03-30T18:35:41Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:35, 30 March 2026
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	For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.		For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.

	For the '''Isochoric process''' <math>\Delta V=0</math>, and thus we have <math>dU = dQ</math>.		For the '''Isochoric process''' <math>\Delta V=0</math>, and thus we have <math>dU = dQ = mc_v dT</math> which gives <math>\Delta Q = m c_v\Delta T</math>.

	<math>		<math>

2026-03-30T18:28:31Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:28, 30 March 2026
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	# Isochoric <math>\Delta Q = m c_v \Delta T</math>		# Isochoric <math>\Delta Q = m c_v \Delta T</math>

	~~The~~ specific heat capacity at constant volume is <math>c_v = \frac{dQ/dT}{m}</math>.		where the specific heat capacity at constant volume is <math>c_v = \frac{dQ/dT}{m}</math>.

2026-03-30T18:28:15Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:28, 30 March 2026
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	# Isobaric <math>Q = \Delta U + p \Delta V</math>		# Isobaric <math>Q = \Delta U + p \Delta V</math>
	# Isochoric <math>\Delta Q = m c_v \Delta T</math>		# Isochoric <math>\Delta Q = m c_v \Delta T</math>

			The specific heat capacity at constant volume is <math>c_v = \frac{dQ/dT}{m}</math>.


			For a closed system, the total change in energy of a system is the sum of the work done and the heat added <math>dU = \delta W + \delta Q</math>, and the reversible work done on a system by changing the volume is <math>\delta W = - p dV</math>. Furthermore, for any transformation of an ideal gas, it is always true that <math>dU = nC_v dT</math>.


	For a closed system, the total change in energy of a system is the sum of the work done and the heat added <math>dU = \delta W + \delta Q</math>, and the reversible work done on a system by changing the volume is <math>\delta W = - p dV</math>.

	If the system is reversible and adiabatic ('''isentropic''') <math>\delta Q = 0</math>, which gives		If the system is reversible and adiabatic ('''isentropic''') <math>\delta Q = 0</math>, which gives
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	</math>		</math>

	~~Furthermore, for any transformation of an ideal gas, it is always true that <math>dU = nC_v dT</math>, giving~~

	<math>		<math>

2026-03-30T18:26:33Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:26, 30 March 2026
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	For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.		For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.

			For the '''Isochoric process''' <math>\Delta V=0</math>, and thus we have <math>dU = dQ</math>.

	<math>		<math>

2026-03-30T18:15:26Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:15, 30 March 2026
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	There are three (3) different processes:		There are three (3) different processes:
	# Isentropic <math>dU = nC_v dT = -pdV</math>		# Isentropic <math>dU = nC_v dT = -pdV</math>
	# Isobaric <math>Q = \Delta U + \~~int p dV~~</math>		# Isobaric <math>Q = \Delta U + p \Delta V</math>
	# Isochoric <math>\Delta Q = m c_v \Delta T</math>		# Isochoric <math>\Delta Q = m c_v \Delta T</math>

2026-03-30T18:15:01Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:15, 30 March 2026
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	</math>		</math>

	For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math>.		For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math> we have <math>W = \int p dV = p \Delta V</math>, and by applying the ideal gas law, we get <math>W = n R \Delta T</math>.

	<math>		<math>

2026-03-30T18:06:20Z

Diesel Cycle and Ideal Gas

← Older revision		Revision as of 21:06, 30 March 2026
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	=== Diesel Cycle and Ideal Gas ===		=== Diesel Cycle and Ideal Gas ===

			There are three (3) different processes:
			# Isentropic <math>dU = nC_v dT = -pdV</math>
			# Isobaric <math>Q = \Delta U + \int p dV</math>
			# Isochoric <math>\Delta Q = m c_v \Delta T</math>


	For a closed system, the total change in energy of a system is the sum of the work done and the heat added <math>dU = \delta W + \delta Q</math>, and the reversible work done on a system by changing the volume is <math>\delta W = - p dV</math>.		For a closed system, the total change in energy of a system is the sum of the work done and the heat added <math>dU = \delta W + \delta Q</math>, and the reversible work done on a system by changing the volume is <math>\delta W = - p dV</math>.

	If the system is reversible and adiabatic (isentropic) <math>\delta Q = 0</math>, which gives		If the system is reversible and adiabatic ('''isentropic''') <math>\delta Q = 0</math>, which gives

	<math>		<math>
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	<math>		<math>
	dU = nC_v dT = -pdV		dU = nC_v dT = -pdV
	</math>		</math>

			For the constant pressure ('''isobaric process''') <math>\Delta p = 0</math>.

			<math>

			</math>

	=== Real gas: Air ===		=== Real gas: Air ===

2026-03-30T17:59:36Z

Real gas: Air

← Older revision		Revision as of 20:59, 30 March 2026
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	Which are widely used in CFD and thermodynamics.		Which are widely used in CFD and thermodynamics.

	Compressibility factor Z (real gas correction). If you want a generalized ideal gas, you often introduce <math>p=Z\rho RT</math>. Where		Compressibility factor Z (real gas correction). If you want a generalized ideal gas, you often introduce <math>p=Z\rho RT</math>. Where
	* Z=1 → ideal gas		* Z=1 → ideal gas
	* Z≠1 → real gas behavior		* Z≠1 → real gas behavior
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	<math>		<math>
	Z=1+\frac{B(T)}V+\frac{C(T)}{V^2}+ \cdots		Z=1+\frac{B(T)}V+\frac{C(T)}{V^2}+ \cdots
	\approx 1+ \frac{B(T)}{RT}p		\approx 1+ \frac{B(T)}{RT}p.
	</math>		</math>


	Mixture-based formulation (more fundamental). Air is a mixture mainly of:		Mixture-based formulation (more fundamental). Air is a mixture mainly of:
	* N₂ (~78%)		* N₂ (~78%)

2026-03-30T17:58:55Z

Real gas: Air