Dans un cylindre, fermé par un piston mobile sur lequel agit...

Dans un cylindre, fermé par un piston mobile sur lequel agit extérieurement la pression atmosphérique, on introduit à la température de $25^{\circ} \mathrm{C} 0,15 \mathrm{~mol}$ de dihydrogène et $0,35 \mathrm{~mol}$ de diazote, puis on bloque le piston dans la position qu'il occupe alors. a) Si on introduit ensuite encore $0,15 \mathrm{~mol}$ de dihydrogène, cette opération fait elle varier, et si oui dans quel sens, > la pression totale dans le cylindre, > la pression partielle du diazote, > la pression partielle du dihydrogène. b) Les réponses seraient-elles modifiées, et comment, si l'on ne bloquait pas le piston?

Dans un cylindre, fermé par un piston mobile sur lequel agit extérieurement la pression atmosphérique, on introduit à la température de $25^{\circ} \mathrm{C} 0,15 \mathrm{~mol}$ de dihydrogène et $0,35 \mathrm{~mol}$ de diazote, puis on bloque le piston dans la position qu'il occupe alors.
a) Si on introduit ensuite encore $0,15 \mathrm{~mol}$ de dihydrogène, cette opération fait elle varier, et si oui dans quel sens,
> la pression totale dans le cylindre,
> la pression partielle du diazote,
> la pression partielle du dihydrogène.
b) Les réponses seraient-elles modifiées, et comment, si l'on ne bloquait pas le piston?

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation relating the pressure, volume, amount (in moles), and temperature of an ideal gas. This relationship allows one to predict how changes in any of the variables (while keeping others constant) affect the gas behavior, making it a cornerstone concept in understanding gas systems.

Dalton's Law of Partial Pressures

Dalton's law states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the individual partial pressures of the component gases. Each gas contributes to the total pressure in proportion to its mole fraction, thus allowing us to analyze changes in the composition of a gas mixture by evaluating its individual partial pressures.

Constant Volume Processes

A constant volume process occurs when the container's volume remains fixed. Under such conditions, any change in the amount of gas or temperature directly impacts the pressure inside the container, as described by the ideal gas law. In fixed-volume scenarios, adding gas increases the pressure proportionately if temperature is maintained constant.

Variable Volume Processes with a Movable Piston

In systems with a movable piston, the volume is allowed to change in response to pressure differences. When the piston is free to move, the system adjusts so that the internal gas pressure matches the external pressure. This introduces equilibria where adding gas may lead to an increase in volume instead of pressure if the system is maintained at constant pressure, highlighting a key difference compared to constant volume conditions.

Transcript

00:01 Belongs to the thermodynamics in which we have two cylinders a and b of equal capacity that is volume is equal v1 equals to v2 and they are connected each other by a stop cock and a contains a get at standard temperature and pressure and b is completely evacuated okay the entire system is thermally insulated so heat cannot be released or gained okay the stopcock is suddenly opened so first for the first part we have to determine the final pressure in the gas a, so pa and pb, we have to determine.

00:36 Now, we can say that the volume available for the gas is doubled in this case, and temperature is, temperature is constant.

00:45 Okay, so from here we can write that pressure p, it will be directly proportional, inversely proportional to the volume because temperature is constant from the ideal gas equation, so volume is doubled, so hence pressure has become half, okay, of the previous way.

00:59 And pressure is 1 atm for the previous value.

01:02 So, pa equals to pb in this condition will be 0 .5 atm.

01:08 So this becomes the answer for the part a of the problem.

01:11 Now moving to the part b, what is the change in the internal energy of the gas? so since temperature is constant, so hence change in the internal energy delta u, it is equal to 0 because it is the function of the temperature only.

01:25 Now moving to the part c, what is the change in the temperature of the gas? so since temperature is constant, so delta t, it is also equals to 0.

01:34 Now, for the part d, do the intermediate state of the system before settling final equilibrium state lies on pvt surface...

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