(a) Explanation The p V diagram of the process is shown below. The work done in an isochoric process is zero. Write the equation for the work done in the isochoric process. W A B = 0 J (I) Here, W A B is the work done in the isochoric process. Write the equation for the work done in the adiabatic process. W B C = p C V C − p B V B γ − 1 (II) Here, W B C is the work done in the adiabatic process, p C is the pressure at point C, V C is the volume at point C, p B is the pressure at point B and V B is the volume at point B and γ is the adiabatic constant. Write the equation for the work done in the isobaric process. W C D = − p C ( V D − V C ) (III) Here, W C D is the work done in the isobaric process and V D is the volume at point D. Write the equation for the work done in an isothermal process. W D A = − n R T ln ( V A V D ) (IV) Here, W D A is the work done in an isothermal process, n is the number of moles, R is the universal gas constant, T is the temperature and V A is the volume at point A. Write the ideal gas equation. p V = n R T (V) Here, p is the pressure and V is the volume. n and R constant. For an isothermal process T is also constant so that right-hand side of the above equation is constant. This implies the left-hand side also must be constant. Rewrite the above equation for the given isothermal process. p A V A = n R T Put the above equation in equation (IV). W D A = − p A V A ln ( V A V D ) (VI) Write the equation for the total work done. W = W A B + W B C + W C D + W D A (VII) Here, W is the total work done. Write the equation for V B . V B = V A (VIII) Write the equation for V C . V C = V A 5 (IX) For an isochoric process V is constant. Rewrite equation (V) for an isochoric process. n R T p = constant Rewrite the above equation for the given isochoric process. n R T A p A = n R T B p B (X) Here, T A is the temperature at point A and T B is the temperature at point B. Write the equation for T B . T B = 2 T A Put the above equation in equation (X). n R T A p A = n R ( 2 T A ) p B p B = 2 p A (XI) Write the equation for the adiabatic process. p B V B γ = p C V C γ Put equations (VIII) and (IX) in the above equation. p B V A γ = p C ( V A 5 ) γ Rewrite the above equation for p C . p C = p B V A γ ( V A 5 ) γ = p B V A γ 1 5 γ V A γ = 5 γ p B Put equation (XI) in the above equation (b) To determine The numerical expression for the work done on the gas during the cycle.

4th Edition

ISBN: 9780135272992

Author: Wolfson

Publisher: VST

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Chapter 18, Problem 34E

(a)

To determine

The expression for the work done on the gas during the cycle.

(b)

To determine

The numerical expression for the work done on the gas during the cycle.

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Chapter 18, Problem 33E

Chapter 18, Problem 35E

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Chapter 18 Solutions

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Ch. 18.2 - Two identical gas-cylinder systems are taken from...Ch. 18.2 - Name the basic thermodynamic process involved when...Ch. 18.3 - The same amount of heat flows into equal volumes...Ch. 18 - Prob. 1FTD Ch. 18 - Prob. 2FTD Ch. 18 - Why cant an irreversible process be described by a...Ch. 18 - Are the initial and final equilibrium states of an...Ch. 18 - Prob. 5FTD Ch. 18 - Figure 18.18 shows two processes, A and B. that...Ch. 18 - When you let air out of a tire, the air seems...

Ch. 18 - Blow on the back of your hand with your mouth wide...Ch. 18 - Three identical gas-cylinder systems are...Ch. 18 - Prob. 10FTD Ch. 18 - Prob. 11E Ch. 18 - Prob. 12E Ch. 18 - A 40-W heat source is applied to a gas sample for...Ch. 18 - Find the rate of heat flow into a system whose...Ch. 18 - In a certain automobile engine, 17% of the total...Ch. 18 - An ideal gas expands from the state (p1, V1) to...Ch. 18 - Repeat Exercise 20 for a process that follows the...Ch. 18 - A balloon contains 0.30 mol of helium. It rises,...Ch. 18 - The balloon of Exercise 22 starts at 100 kPa...Ch. 18 - How much work does it take to compress 2.5 mol of...Ch. 18 - By what factor must the volume of a gas with =...Ch. 18 - Prob. 22E Ch. 18 - A carbon-sequestration scheme calls for...Ch. 18 - A gas mixture contains 2.5 mol of O2 and 3.0 mol...Ch. 18 - A mixture of monatomic and diatomic gases has...Ch. 18 - What should be the approximate specific-heat ratio...Ch. 18 - Prob. 27E Ch. 18 - Prob. 28E Ch. 18 - Example 18.2: A gas bubble develops from...Ch. 18 - Prob. 30E Ch. 18 - Example 18.2: A spherical balloon is placed inside...Ch. 18 - Prob. 32E Ch. 18 - Example 18.4: An ideal gas with γ = 40 and...Ch. 18 - Prob. 34E Ch. 18 - Example 18.4: An ideal gas with γ = 1.40 is...Ch. 18 - An ideal gas expands to 10 times its original...Ch. 18 - During cycling, the human body typically releases...Ch. 18 - A 0.25-mol sample of ideal gas initially occupies...Ch. 18 - As the heart beats, blood pressure in an artery...Ch. 18 - It takes 1.5 kJ to compress a gas isothermally to...Ch. 18 - A gas undergoes an adiabatic compression during...Ch. 18 - A gas with = 1.40 occupies 6.25 L when its at...Ch. 18 - A gas sample undergoes the cyclic process ABCA...Ch. 18 - Prob. 44P Ch. 18 - A gasoline engine has compression ratio 8.5 (sec...Ch. 18 - By what factor must the volume of a gas with =...Ch. 18 - Volvos B5340 engine, used in the V70 series cars,...Ch. 18 - A research balloon is prepared for launch by...Ch. 18 - Prob. 49P Ch. 18 - By what factor does the internal energy of an...Ch. 18 - A 3.50-mol sample of ideal gas with molar specific...Ch. 18 - Prove that the slope of an adiabat at a given...Ch. 18 - An ideal gas with = 1.67 starts at point A in...Ch. 18 - The gas of Example 18.4 starts at state A in Fig....Ch. 18 - The gas of Example 18.4 starts at state A in Fig....Ch. 18 - Prob. 56P Ch. 18 - Youre the product safety officer for a company...Ch. 18 - Figure 18.22 shows data and a fit curve from an...Ch. 18 - Gasoline and diesel engines often use...Ch. 18 - A gas with = 7/5 is at 273 K when its compressed...Ch. 18 - An ideal gas with = 1.3 is initially at 273 K and...Ch. 18 - The curved path in Fig. 18.23 lies on the 350-K...Ch. 18 - Repeat part (a) of Problem 62 for the path ACDA in...Ch. 18 - A gas mixture contains monatomic argon and...Ch. 18 - How much of a triatomic gas with Cv = 3R would you...Ch. 18 - An 8.5-kg rock at 0C is dropped into a...Ch. 18 - A piston-cylinder arrangement containing 0.30 mol...Ch. 18 - Experimental studies show that the pV curve for a...Ch. 18 - Show that the application of Equation 18.3 to an...Ch. 18 - Prob. 70P Ch. 18 - Prob. 71P Ch. 18 - The table below shows measured values of pressure...Ch. 18 - Air with initial volume V0 = 4.50 L and initial...Ch. 18 - A real gas is more accurately described using the...Ch. 18 - Repeat Exercise 20 for an expansion along the path...Ch. 18 - The adiabatic lapse rate is the rate at which air...Ch. 18 - A power plant extracts thermal energy from its...Ch. 18 - Prob. 78P Ch. 18 - One scheme for reducing greenhouse-gas emissions...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...

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