Question

Визначте якою буде абсолютна температура певної маси ідеального газу , якщо тиск газу збільшити на 25%, а об'єм зменшити на 20%.початкова температура газу =300К

Answer 1

Дано:
T₁ = 300 К
p₁
V₁
p₂ = 1,25·p₁
V₂ = V₁ / 1,2
__________
T₂ - ?

Объединенный газовый закон:
p₁·V₁ / T₁ = p₂·V₂ / T₂

p₁·V₁ / 300 = 1,25·p₁· V₁ / (1,2·T₂)
1 / 300 = 1,25 / (1,2·T₂)

Отсюда:
T₂ = 300·1,25 / 1,2 =  312,5 К

Answer 2

Calculation of Absolute Temperature

To calculate the absolute temperature of a certain mass of an ideal gas after increasing the pressure by 25% and decreasing the volume by 20%, we can use the combined gas law equation:

P1V1 / T1 = P2V2 / T2

Where: - P1 is the initial pressure - V1 is the initial volume - T1 is the initial temperature - P2 is the final pressure (25% increase from the initial pressure) - V2 is the final volume (20% decrease from the initial volume) - T2 is the final temperature (what we want to find)

Given: - Initial temperature (T1) = 300 K - Pressure increase = 25% - Volume decrease = 20%

Let's substitute the given values into the equation and solve for T2:

P1V1 / T1 = P2V2 / T2

P1 = P2 + (25% of P2) = P2 + 0.25P2 = 1.25P2

V1 = V2 - (20% of V2) = V2 - 0.2V2 = 0.8V2

Substituting these values into the equation:

(1.25P2)(0.8V2) / T1 = P2V2 / T2

Simplifying:

1.25P2V2 / T1 = P2V2 / T2

Cross-multiplying:

1.25P2V2 * T2 = P2V2 * T1

Canceling out the common terms:

1.25T2 = T1

Solving for T2:

T2 = T1 / 1.25

Substituting the given initial temperature (T1 = 300 K) into the equation:

T2 = 300 K / 1.25

Calculating:

T2 = 240 K

Therefore, the absolute temperature of the gas after increasing the pressure by 25% and decreasing the volume by 20% will be 240 K.