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Chapter 3: Q. 3.28 (page 113)

A liter of air, initially at room temperature and atmospheric pressure, is heated at constant pressure until it doubles in volume. Calculate the increase in its entropy during this process.

Short Answer

Expert verified

The increase in entropy is816.51JK-1.

Step by step solution

01

Given Information

Pressure =P=101325Pa

Temperature =T=300K

Volume =V=1L

Heat capacity at constant pressure=Cp=29JK-1

02

Calculation

For an ideal gas, as the volume doubles, the temperature must also double.

The change in entropy is given as:

螖S=鈭�TiTfQT螖S=鈭�TiTfCpdTT螖S=Cpln[T]TiTf螖S=CplnTfTi螖S=Cpln2TiTi螖S=Cpln2

For the number of molecules in one liter of air,

n=PVRTn=101325脳18.314脳300n=40.62mol

Hence, change in entropy for one liter of air can be calculated as:

螖S=nCpln2螖S=40.62脳29脳ln2螖S=816.51JK-1

03

Final answer

Hence, the entropy of air will be 816.51JK-1when air is heated at constant pressure and its volume doubles.

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Most popular questions from this chapter

A cylinder contains one liter of air at room temperature ( 300K) and atmospheric pressure 105N/m2. At one end of the cylinder is a massless piston, whose surface area is 0.01m2. Suppose that you push the piston in very suddenly, exerting a force of 2000N. The piston moves only one millimeter, before it is stopped by an immovable barrier of some sort.

(a) How much work have you done on this system?

(b) How much heat has been added to the gas?

(c) Assuming that all the energy added goes into the gas (not the piston or cylinder walls), by how much does the internal energy of the gas increase?

(d) Use the thermodynamic identity to calculate the change in the entropy of the gas (once it has again reached equilibrium).

In Problem 2.32you computed the entropy of an ideal monatomic gas that lives in a two-dimensional universe. Take partial derivatives with respect to U,A, and N to determine the temperature, pressure, and chemical potential of this gas. (In two dimensions, pressure is defined as force per unit length.) Simplify your results as much as possible, and explain whether they make sense.

Use the result of Problem 2.42 to calculate the temperature of a black hole, in terms of its mass M. (The energy is Mc2. ) Evaluate the resulting expression for a one-solar-mass black hole. Also sketch the entropy as a function of energy, and discuss the implications of the shape of the graph.

Verify every entry in the third line of Table 3.2 (starting with N鈫�=98.

Fill in the missing algebraic steps to derive equations 3.30, 3.31, and 3.33.
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