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We have an experimental chamber with a volume of [tex]V=66.5 \, \text{L}[/tex] filled with [tex]m=53.7 \, \text{g}[/tex] of ideal gas having molecular mass [tex]20.6 \, \text{g/mol}[/tex]. The chamber has perfect thermal isolation from its surroundings except for a small window with an area of [tex]A=28.2 \, \text{cm}^2[/tex], thermal conductivity of [tex]k=0.555 \, \text{W/(m} \cdot \text{K)}[/tex], and thickness of [tex]\ell=5.39 \, \text{mm}[/tex]. A heater on the inside of the chamber keeps the interior at a temperature of [tex]T_H=297^{\circ} \text{C}[/tex].

a. How many moles of gas do we have in the chamber?

b. If the lab is kept at a constant temperature of [tex]T_C=20.8^{\circ} \text{C}[/tex], what is the energy lost by the chamber every minute through the window?

c. What is the gauge pressure of gas on the inside of the chamber with respect to the pressure on the outside?

d. A leak occurs and [tex]\Delta m=14.4 \, \text{g}[/tex] of gas escapes before it is caught. What is the new gauge pressure on the inside of the chamber?

To continue, please give the initial number of moles of gas in the chamber (part a) in units of mol.

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Sagot :

GinnyAnsweridn
To find the number of moles of gas in the chamber, we need to use the following formula:

[tex]\[ n = \frac{m}{M} \][/tex]

where:
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( m \)[/tex] is the mass of the gas,
- [tex]\( M \)[/tex] is the molecular mass of the gas.

Given the values:
- [tex]\( m = 53.7 \)[/tex] grams (mass of the gas),
- [tex]\( M = 20.6 \)[/tex] grams per mole (molecular mass of the gas),

we can plug these into the formula:

[tex]\[ n = \frac{53.7 \, \text{g}}{20.6 \, \text{g/mol}} \][/tex]

Performing this division, we get:

[tex]\[ n \approx 2.6068 \, \text{mol} \][/tex]

Thus, the initial number of moles of gas in the chamber is approximately [tex]\( 2.6068 \, \text{mol} \)[/tex].
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