Concept explainers
Derive expressions for (a) Δu, (b) Δh, and (c) Δs for a gas whose equation of state is P(v − a) = RT for an isothermal process.
(a)
To drive an expression of
Answer to Problem 42P
The expression of
Explanation of Solution
Write the equation of state of the given gas.
Here, the temperature is
Write the general expression for change in internal energy
Here, the internal energy at state 1, 2 is
Rearrange the Equation (I) to obtain
Conclusion:
Partially differentiate the Equation (III) with respect to temperature by keeping the specific volume as constant.
Substitute
For an isothermal process, the temperature is kept constant.
The differential temperature or change in temperature becomes zero.
Substitute
Thus, the expression of
(b)
To drive an expression of
Answer to Problem 42P
The expression of
Explanation of Solution
Write the general expression for change in enthalpy
Here, the enthalpy at state 1, 2 is
Rearrange the Equation (V) to obtain
Conclusion:
Partially differentiate the Equation (VI) with respect to temperature by keeping the pressure as constant.
Substitute
For an isothermal process, the temperature is kept constant.
The differential temperature or change in temperature becomes zero.
Substitute
Thus, the expression of
(c)
To drive an expression of
Answer to Problem 42P
The expression of
Explanation of Solution
Write the general expression for change in entropy
Here, the entropy at state 1, 2 is
Conclusion:
Substitute
For an isothermal process, the temperature is kept constant.
The differential temperature or change in temperature becomes zero.
Substitute
Thus, the expression of
Want to see more full solutions like this?
Chapter 12 Solutions
THERMODYNAMICS: AN ENGINEERING APPROACH
- Using the Maxwell relation and the ideal-gas equation of state, determine a relation for (ds/dv)T for an ideal gas Answer is R/varrow_forward7-Nitrogen is present in a closed system at a pressure of 830 kPa and a temperature of 380°C.If nitrogen is expanded isentropically to a pressure of 115 kPa, which of the following will have the lowest temperature? (take cazo = 1.4) A) 308,7 K B) 371,2 K C) 220,6 K D) 216,0 K E) 310,4 Karrow_forwardAn ideal gas at 27°C expands isothermally and reversibly from 10 to 1 bar against a pressurethat is gradually reduced.arrow_forward
- Describe the equilibrium condition in terms of the entropy changes of a system and its surroundings. What does this de-scription mean about the entropy change of the universe?arrow_forwardFor methane at 1500 psia and 168F, determine: (A) z-factor (B) isothermal compressibilityarrow_forwardDerive the Bernoulli equation when the compressibility effects are not negligible for an ideal gas undergoing an (a) Isothermal process (b) Isentropic process? Step by step solve this questionarrow_forward
- A 2.00 - mol sample of an ideal diatomic gas at a pressure of 1.00 atm and temperature of 440 K undergoes a process in which its pressure increases linearly with temperature, use P = Po + aT . The final temperature and pressure are 720 K and 1.60 atm. Determine (e) the change in internal energy, (b) the work done by the gas, and (c) the heat added to the gas. (Assume five active degrees of freedom . )arrow_forwardSelect all correct statements below based on the increase of entropy principle__________ A. The entropy of an isolated system during a process always increases B. C. D. E.arrow_forwardDraw the T-S diagram and enumerate the thermodynamic analysis of each state point.arrow_forward
- Dry saturated steam at 200 bar expands isothermally and reversibly to a pressure of 10 bar. Calculate the heat supplied and the work done per kg of steam.arrow_forward4. An ideal gas at 270c and pressure of 1atm. Is comressed isothermally from a volume of 2 m3 to 1m3. It is then expand reversibly and adiabatically to four times its original volume. Calculat the final pressure and temperature of the gas if ¥=5/3.arrow_forwardDetermine the properties of propane in gaseous state with the help of generalizedcompressibility charts according to the conditions given below. Compare the results obtainedwith the ideal gas equation of state.a) Specific volume at 7 MPa, 150 ℃b) Pressure at 150 ℃, 0.006 m3/kgc) Temperature at 0.006 m3/kg, 7 MPaarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY