Question

В двух вертикальных цилиндрах находятся при одной температуре две равные массы идеального газа. Подвижный поршень первого цилиндра в 3 раза тяжелее, чем во втором цилиндре. Газ в цилиндрах нагрели до одной и той же температуры. В первом цилиндре газ совершил работу 100 Дж. Какую работу совершил газ во втором цилиндре?

Answer 1

Ответ:

см фото

Объяснение:

Answer 2

Problem Analysis

We are given two vertical cylinders containing equal masses of an ideal gas at the same temperature. The movable piston in the first cylinder is three times heavier than the piston in the second cylinder. The gas in both cylinders is heated to the same temperature, and the gas in the first cylinder performs 100 J of work. We need to determine the work done by the gas in the second cylinder.

Solution

To solve this problem, we can use the principle of work done by a gas in a cylinder. The work done by a gas is given by the equation:

Work = Pressure x Change in Volume

Since the temperature and the amount of gas are the same in both cylinders, the pressure is also the same. Therefore, the work done by the gas in each cylinder is directly proportional to the change in volume.

Let's assume that the change in volume in the first cylinder is V1 and the change in volume in the second cylinder is V2. Since the gas in both cylinders is at the same temperature, we can write:

V1 = V2

Now, let's assume that the area of the piston in the first cylinder is A1 and the area of the piston in the second cylinder is A2. Since the pistons have different masses, we can write:

A1 x Δh1 = A2 x Δh2

where Δh1 and Δh2 are the changes in height of the pistons in the first and second cylinders, respectively.

Since the piston in the first cylinder is three times heavier than the piston in the second cylinder, we can write:

Δh1 = 3 x Δh2

Substituting this into the previous equation, we get:

A1 x (3 x Δh2) = A2 x Δh2

Simplifying, we find:

3 x A1 = A2

Now, let's consider the work done by the gas in each cylinder. We know that the work done by the gas in the first cylinder is 100 J. Therefore, we can write:

Work1 = Pressure x ΔV1 = 100 J

Since the pressure is the same in both cylinders and ΔV1 = ΔV2, we can write:

Pressure x ΔV2 = 100 J

Finally, substituting the relationship between the areas of the pistons, we get:

Pressure x (A2 x Δh2) = 100 J

Since we know that Pressure x (A2 x Δh2) is the work done by the gas in the second cylinder, we can conclude that the work done by the gas in the second cylinder is also 100 J.

Therefore, the work done by the gas in the second cylinder is 100 J.

Answer

The gas in the second cylinder also performs 100 J of work.