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(I) One liter of air is cooled at constant pressure until its volume is halved, and then it is allowed to expand isothermally back to its original volume. Draw the process on a PV diagram.

Short Answer

Expert verified

The PV diagram of the process is shown below.

Step by step solution

01

Concepts

The process is called isobaric as the pressure is constant.

For the isothermal expansion, the gas follows Boyle's law.

02

Given data

The initial volume of the gas is 1 L.

03

PV diagram 

The volume of the gas becomes 0.5 L at the end of the first compression.

The PV diagram of the process is shown below.

Here, the pressure of the gas decreases during the isothermal expansion.

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Most popular questions from this chapter

Question: (a) At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate heat input of the second. The operating temperatures of the first are 750ยฐC and 440ยฐC, and of the second 415ยฐC and 270ยฐC. If the heat of combustion of coal is \({\bf{2}}{\bf{.8 \times 1}}{{\bf{0}}^{\bf{7}}}\;{{\bf{J}} \mathord{\left/{\vphantom {{\bf{J}} {{\bf{kg}}}}} \right.} {{\bf{kg}}}}\) at what rate must coal be burned if the plant is to put out 950 MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency. (b) Water is used to cool the power plant. If the water temperature is allowed to increase by no more than 4.5 Cยฐ, estimate how much water must pass through the plant per hour.

Question: An ideal gas undergoes an isobaric compression and then an isovolumetric process that brings it back to its initial temperature. Had the gas undergone one isothermal process instead,

(a) the work done on the gas would be the same.

(b) the work done on the gas would be less.

(c) the work done on the gas would be greater.

(d) Need to know the temperature of the isothermal process.

It has been suggested that a heat engine could be developed that made use of the temperature difference between water at the surface of the ocean and water several hundred meters deep. In the tropics, the temperatures may be 27ยฐC and 4ยฐC, respectively.

(a) What is the maximum efficiency such an engine could have?

(b) Why might such an engine be feasible in spite of the low efficiency?

(c) Can you imagine any adverse environmental effects that might occur?

An ideal gas undergoes an isothermal process. Which of the following statements are true? (i) No heat is added to or removed from the gas. (ii) The internal energy of the gas does not change. (iii) The average kinetic energy of the molecules does not change.

(a) (i) only.

(b) (i) and (ii) only.

(c) (i) and (iii) only.

(d) (ii) and (iii) only.

(e) (i), (ii), and (iii).

(f) None of the above.

Can mechanical energy ever be transformed completely into heat or internal energy? Can the reverse happen? In each case, if your answer is no, explain why not, if yes, give one or two examples.

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