Question

Одноатомному газу (V=2 моль) предано количество теплоты 1,2 кДж. При этом газ совершил работу 600 Дж, На сколько изменилась температура газа?

Answer 1

полученное тепло Q пошло на совершение работы и повышение внутренней энергии

Q=∆U + A  ; ∆U=Q-A

для одноатомного газа изменение внутренней энергии считаем по ф-ле

∆U = 3/2vR∆T

отсюда

∆T=∆U*2/(3vR)=2(Q-A)/(3vR)=2(1200-600)/(3*2*8.31)  =24 K

Answer 2

Calculation of Temperature Change

To determine the change in temperature of the gas, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The equation for the first law of thermodynamics is:

ΔU = Q - W

Where: - ΔU is the change in internal energy of the gas - Q is the heat added to the gas - W is the work done by the gas

In this case, the heat added to the gas is given as 1.2 kJ (kilojoules) and the work done by the gas is given as 600 J (joules).

Converting the heat from kilojoules to joules: 1.2 kJ = 1200 J

Substituting the values into the equation: ΔU = 1200 J - 600 J ΔU = 600 J

The change in internal energy of the gas is 600 J.

The change in internal energy of an ideal gas is related to its temperature change through the equation:

ΔU = nCvΔT

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

In this case, the gas is a monoatomic gas with a volume of 2 moles.

The molar heat capacity at constant volume for a monoatomic gas is given by:

Cv = (3/2)R

Where R is the ideal gas constant.

Substituting the values into the equation: 600 J = 2 mol * (3/2)R * ΔT

Simplifying the equation: 600 J = 3R * ΔT

Dividing both sides of the equation by 3R: ΔT = 600 J / (3R)

Now, we need to find the value of the ideal gas constant, R. The value of R depends on the units used for pressure and volume. The most commonly used value of R is 8.314 J/(mol·K).

Substituting the value of R into the equation: ΔT = 600 J / (3 * 8.314 J/(mol·K))

Calculating the value of ΔT: ΔT ≈ 24.1 K

Therefore, the temperature of the gas changed by approximately 24.1 Kelvin.

Please note that the above calculation assumes that the gas behaves ideally and that there are no other factors affecting the temperature change.