Chapter 3: Q16E (page 610)

Three moles of an ideal gas are in a rigid cubical box with sides of length 0.300 m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0°C? (b) What is the force when the temperature of the gas is increased to 100.0°C?

Short Answer

Expert verified

Force acting is $2.43 \times 10^{4} N$ at each side.
$3.101 \times 10^{4} N$ of force when the temperature of the gas is increased at $100 ° C$

Step by step solution

Step: 1

$n = 3 m o l, L = 0.3 m, T = 293 K, V = 0.027 m^{3}$

Force acting on each side

F=P.A

A is the area of each side and P is pressure applied by the gas

$P V = n R T P = \frac{n R T}{V} = \frac{3 \times 8.315 \times 293}{0.027} = 27.069 \times 10^{4}$

Force (F) by using Pressure (P)

$F = P \times A = 27.069 \times 10^{4} \times (0.3 \times 0.3) = 2.43 \times 10^{4} N$

Force acting is $2.43 \times 10^{4} N$ at each side.

Step: 2

The ideal gas equation thus the relation between P and T

$P \propto T$

Therefore,

$F \propto T$

Temperature increases force increases, the temperature increases to 373K

The force (F)

$\frac{F_{1}}{F_{2}} = \frac{T_{1}}{T_{2}} F_{2} = \frac{F_{1} \times T_{2}}{T_{1}} = \frac{2.43 \times 10^{4} \times 373}{293} = 3.101 \times 10^{4} N$

$3.101 \times 10^{4} N$ of force when the temperature of the gas is increased at $100 ° C$ .

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Three moles of an ideal gas are in a rigid cubical box with sides of length 0.300 m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0°C? (b) What is the force when the temperature of the gas is increased to 100.0°C?

Short Answer

Step by step solution

Step: 1

Step: 2

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