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Chapter 3: Q1E (page 639)

Two moles of an ideal gas are heated at constant pressure from T = 27掳C to T = 107掳C. (a) Draw a pV-diagram for this process. (b) Calculate the work done by the gas

Short Answer

Expert verified

(a) The diagram for the process is:

(b) The work done by the two molecules of an ideal gas when heated at constant pressure is 1330.3J

Step by step solution

01

About Ideal Gas equation and work done in a volume change at constant pressure

The Ideal gas equation is given by:

Where, p is the pressure of the gas,V The volume of the gas,number of moles, R is Ideal gas constant or 8.314472J/mol.K , and T is temperature.

The work done by gas in a volume change at constant pressure is:

W=pA鈭�x=p鈭�V鈬�W=pV2-V1=p鈭�V

Where, p is pressure of the gas, V2is final volume, V1is initial volume.

02

The pV diagram of the process

Therefore, the pV diagram of the process is liner.

03

Work done by the two moles of an ideal gas

Given,T2=102掳C

T1=27掳C

From above we have seen that the equation of an Ideal gas is: PV = nRT , here n,P,R are constant

P鈭�V=nR鈭�TW=pV2-V1P鈭�V=nR鈭�T=28.314472J/(mol.K)(107-27)K=1330.3J

Therefore, the work done by the two molecules of the ideal gas is 1330.3J

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Most popular questions from this chapter

A cylinder with a frictionless, movable piston like that shown in Fig. 19.5 contains a quantity of helium gas. Initially the gas is1.00脳105Pa at 300 K and and occupies a volume of 1.50 L. The gas then undergoes two processes. In the first, the gas is heated and the piston is allowed to move to keep the temperature at . This continues until the pressure reaches 2.50脳104Pa. In the second process, the gas is compressed at constant pressure until it returns to its original volume of 1.50 L. Assume that the gas may be treated as ideal. (a) In a pV-diagram, show both processes. (b) Find the volume of the gas at the end of the first process, and the pressure and temperature at the end of the second process. (c) Find the total work done by the gas during both processes. (d) What would you have to do to the gas to return it to its original pressure and temperature?

You build a heat engine that takes 1.00 mol of an ideal diatomic gas through the cycle shown in Fig. P20.39. (a) Show that process ab is an isothermal compression. (b) During which process(es) of the cycle is heat absorbed by the gas? During which process(es) is heat rejected? How do you know? Calculate (c) the temperature at points a, b, and c; (d) the net heat exchanged with the surroundings and net work done by the engine in one cycle; (e) the thermal efficiency of the engine.

For a gas of nitrogen moleculesN2 , what must the temperature be if 94.7% of all the molecules have speeds less than (a) 1500 m/s (b) 1000 m/s (c) 500 m/s ? Use Table 18.2. The molar mass of N2 is 28 g/mol.

You propose a new temperature scale with temperatures given in 掳M. You define 0.0掳M to be the normal melting point of mercury and 100.0掳M to be the normal boiling point of mercury. (a) What is the normal boiling point of water in 掳M? (b) A temperature change of 10.0 掳M corresponds to how many 掳C?

Many automobile engines have cast-iron cylinders and aluminium pistons. What kinds of problems could occur if the engine gets too hot? (The coefficient of volume expansion of cast iron is approximately the same as that of steel.)
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