Question

Ідеальний газ при нагріванні на 20 К виконав роботу 831 Дж. Записати перший закон термодинаміки для цього процесу і визначити кількість молів газу, вважаючи процез ізобарним

Answer 1

Дано: ΔT=20К
R=8,31Дж/ К*моль
А=831 Дж
При изобарном процессе давление Р=const, поэтому 1 закон термодинамики имеет вид: ΔU =Q-A,  ΔU =Q -PΔV или ΔU=Q-νRΔT.
Так как  А=νRΔT, то ν =А/ RΔT, ν =831 / 8,31*20=5 моль
Ответ: 5 моль 

Answer 2

First Law of Thermodynamics for Ideal Gas

When an ideal gas is heated at constant pressure (an isobaric process), the first law of thermodynamics can be expressed as:

Q = ΔU + W

Where: - Q is the heat added to the system, - ΔU is the change in internal energy of the system, - W is the work done by the system on the surroundings.

Calculation of the Number of Moles of Gas

Given that the ideal gas performed work of 831 J when heated by 20 K, we can use the first law of thermodynamics to calculate the number of moles of the gas.

The work done by the gas is given as 831 J, and the change in temperature is 20 K.

Using the equation Q = ΔU + W, where Q is the heat added to the system, and ΔU is the change in internal energy, we can rearrange the equation to solve for ΔU:

ΔU = Q - W

Substituting the given values: ΔU = 831 J - 831 J = 0

The change in internal energy, ΔU, is 0, as the work done is equal to the heat added.

Now, to find the number of moles of the gas, we can use the equation:

ΔU = nCvΔT

Where: - n is the number of moles of the gas, - Cv is the molar specific heat at constant volume, - ΔT is the change in temperature.

Given that the process is isobaric, we can use the relationship between the molar specific heat at constant pressure (Cp) and the molar specific heat at constant volume (Cv):

Cp - Cv = R

Where R is the gas constant.

Substituting the values into the equation and solving for n: 0 = nCvΔT n = 0 / CvΔT

This calculation requires the specific heat at constant volume (Cv) for the gas, which is not provided in the given information. Therefore, without the specific value of Cv, it is not possible to determine the number of moles of the gas.