   Chapter 12, Problem 24P

Chapter
Section
Textbook Problem

An ideal gas expands at constant pressure. (a) Show that PΔ V = nRΔT. (b) If the gas is monatomic, start from the definition of internal energy and show that Δ U = 3 2 Wenv, where Wenv is the work done by the gas on its environment. (c) For the same monatomic ideal gas, show with the first law that Q = 5 2 Wenv. (d) Is it possible for an ideal gas to expand at constant pressure while exhausting thermal energy? Explain.

(a)

To determine

To show that: P(ΔV)=nR(ΔT) for an ideal gas expands at constant pressure.

Explanation

The ideal gas law is,

PV=nRT

• P is the pressure of the gas
• V is the volume of the gas
• n is the amount of gas in moles
• R is the universal gas constant
• T is the absolute temperature

From the ideal gas law,

PiVi=nRTi       (1)

PfVf=nRTf       (2)

When ideal gas expands at constant pressure,

Pi=Pf=P

Thus, equation (1) and (2) gives

PVi=nRT

(b)

To determine

To show that: for a monatomic gas, ΔU=32Wenv .

(c)

To determine

To show that: for a monatomic gas, Q=52Wenv .

(d)

To determine
whether it is possible for an ideal gas to expand at constant pressure while exhausting thermal energy.

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