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$\bullet$ Three moles of an ideal gas are in a rigid cubical box with sides of length 0.200 $\mathrm{m} .$ (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is $20.0^{\circ} \mathrm{C}$ ? (b) What is the force when the temperature of the gas is increased to $100.0^{\circ} \mathrm{C} ?$

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$(a) 3.99 \times 10^{4} N\left($ b) $4.65 \times 10^{4} N\right.$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

Cornell University

University of Washington

Hope College

University of Sheffield

Lectures

03:15

In physics, the second law of thermodynamics states that the total entropy of an isolated system can only increase over time. The total entropy of a system can never decrease, and the entropy of a system approaches a constant value as the temperature approaches zero.

03:25

The First Law of Thermodynamics is an expression of the principle of conservation of energy. The law states that the change in the internal energy of a closed system is equal to the amount of heat energy added to the system, minus the work done by the system on its surroundings. The total energy of a system can be subdivided and classified in various ways.

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Three moles of an ideal ga…

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this's Chapter 50 of Problem number six will be half three moles of gas confined in a queue. Who dimension is 30.2 meters of import a Mrs three most gas right In part, they were asked to calculate the force step the gas exerts on each six sides of the box when the temperature is 20 senses. So we're asked attacking the force. First of all, first for forgiving area is going to give us the pressure of the gas. And how are we going to get the pressure? We're going to use the ideal gas law and then we're going to come here and play it in for the area of one side of the cube and then calculate the force. Right? So from the ideal gas law, then pressure times balding with gas peoples to the member moles and the ideal guest constant in times the temperature of the gas safety divide both sides by the volume. Then we get people's an RT over V. The in this case is the volume of the gas which is finding and cube than the air. The walling with Cuba is going to be all cute, right? So we can plug that being here. All right, now go on back to the force equation. Multiply both sides of this equation by the area. Then we have forced equals pressure times area. So since for caf s to calculate the force exerted on one side of the cue, the the area that we're dealing with is elsewhere, right? It's basically a square. So now pressure times elsewhere then is gonna give us the force. By the way, we know what pressure is. Weaken. Just substitute for so and far too youthful. Burkle Cube times elsewhere, then is gonna give us the force. So as you can see these cancel apt. We have one alley denominator. Marty Korver out is going to give us the force now, if you like land for in American values Three moles of gas and then the ideal gas constant here. Be careful. The minutes, All the ice ideal guest constant that you're using. So here I'm going to use a 8.1. Pardon me. 8.31 He'd 0.31 31 or five jewels per mold her Calvin And in this case, well again, we need to do the conversion. So we have to write the temperature in terms of Calvin, as you can see. So it's gonna be 273 plus 20 1,000 divided five 0.2 meters. So if you're here, what you're getting unit wise eyes going. Toby knows we're gonna cancel out Jules per Jules per meter, which is going to give us the Newtons. Right? So it's going to be 3.66 times center for or mutants right now in part B. We're going to do pretty much the same thing. Were asked the same thing. The forces that the gas exerts on one side of this cube when the O the temperature is instead of 20 Celsius, this time temperature is going to be 100 Celsius. So now our B, the temperature is 100 Celsius. Nothing is going to change for stealing is the same expression that we have here for force and Artie over l. Let's copy it, hand her tea over elf again. And still three most our is 8.3145 jewels Purple more for jasmine. This time it's 273 plus 100 cal divided by point. It now then what? We has forces for 0.65 times century before amusements compare this number to the number that we found here. So the brand of the temperature is the greater the pressure. Then we have greater force exerted on outside of the cube.

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