Question

Газ имеет объем 1 м ^ 3 при давлении 10 ^ 5 Па. Каков объем этого газа при давлении 5 МПа, когда температура не меняется?

Answer 1

Дано:

V$_{1}$ = 1 м³

p$_{1}$ = $10^{5}$ Па

p$_{2}$ = 5 МПа = $5 * 10^{6}$ Па

T = const

Найти: V$_{2}$.

Решение:

По условию температура не меняется. По закону Бойля-Мариотта:

$p_{1}V_{1} = p_{2} V_{2}\\\\V_{2} = \frac{p_{1}V_{1}}{p_{2}} = \frac{10^{5}*1}{5*10^{6}} = \frac{1}{50}$ = 0,02 м³.

Ответ: 0,02 м³.

Answer 2

Calculation of Gas Volume

To calculate the volume of a gas at a different pressure while keeping the temperature constant, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.

According to Boyle's Law, the product of the initial pressure and volume is equal to the product of the final pressure and volume:

P1 * V1 = P2 * V2

Where: - P1 is the initial pressure of the gas - V1 is the initial volume of the gas - P2 is the final pressure of the gas - V2 is the final volume of the gas

In this case, we have the initial volume (V1) as 1 m^3 and the initial pressure (P1) as 10^5 Pa. We need to find the final volume (V2) when the pressure (P2) is 5 MPa (5 * 10^6 Pa).

Using Boyle's Law, we can rearrange the equation to solve for V2:

V2 = (P1 * V1) / P2

Substituting the given values:

V2 = (10^5 Pa * 1 m^3) / (5 * 10^6 Pa)

Simplifying the expression:

V2 = 0.02 m^3

Therefore, the volume of the gas at a pressure of 5 MPa, with the temperature remaining constant, is 0.02 m^3.