   Chapter 12, Problem 23P

Chapter
Section
Textbook Problem

An ideal monatomic gas expands isothermally from 0.500 m3 to 1.25 m3 at a constant temperature of 675 K. If the initial pressure is 1.00 × 105 Pa, find (a) the work done on the gas, (b) the thermal energy transfer Q, and (c) the change in the internal energy.

(a)

To determine
the work done on the gas.

Explanation

Given Info:

The initial volume of the gas is 0.500m3 .

The final volume of the gas is 1.25m3 .

The initial pressure of the gas is 1.00×105Pa .

Formula to calculate the work done on the gas is,

W=nRTln(VfVi)

• n is the amount of gas in moles
• R is the universal gas constant
• T is the absolute temperature
• Vf is the finial volume of the gas
• Vi is the initial volume of the gas

Since, when the temperature is constant; ideal gas law is,

PiVi=PfVf=nRT

Thus, the work done on the gas is,

W=PiViln(VfVi)

• Pi is the initial pressure of the gas
• Vi is the initial volume of the gas

Substitute 1

(b)

To determine
the thermal energy transfer, Q.

(c)

To determine
the change in internal energy of the ideal gas.

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