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Chapter 5

Q. 5.6

Argon is an inert gas used in lightbulbs to retard the vaporization of the tungsten filament. A certain lightbulb containing argon at 1.20 atm and 18°C is heated to 85°C at constant volume. Calculate its final pressure (in atm). Electric lightbulbs are usually filled with argon.

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Strategy The temperature and pressure of argon change but the amount and volume of gas remain the same. What equation would you use to solve for the final pressure? What temperature unit should you use?

 

Step-by-Step

Verified Solution

Because  n_{1} = n_{2}   and   V_{1} = V_{2}, Equation (5.9) becomes

\frac{P_1 V_1}{n_1 T_1}=\frac{P_2 V_2}{n_2 T_2}     (5.9)

\frac{P_{1}}{T_{1}}= \frac{P_{2}}{T_{2}}

which is Charles’s law [see Equation (5.6)] \frac{P_{1}}{T_{1}}= \frac{P_{2}}{T_{2}}

. Next we write

\begin{matrix} Initial  Conditions & & Final  Conditions\\\hline \\ P_{1}=1.20  amt & & P_{2}=? \\ T_{1}=(18+273)  K=291  K & & T_{1}=(85+273)  K=358  K \end{matrix}

 

The final pressure is given by

P_{2}=P_{1} \times\frac{T_{2}}{T_{1}}

 

=1.20  atm \times \frac{358  K}{291  K}

=1.48  atm

Check At constant volume, the pressure of a given amount of gas is directly proportional to its absolute temperature. Therefore, the increase in pressure is reasonable.