A gas undergoing a Carnot cycle with an efficiency of 25%

Let us solve the problem of the work done by a gas during isothermal compression, if it is known that the gas undergoes a Carnot cycle and its efficiency is 25%, and during isothermal expansion the gas produces 240 J of work.

Using the Carnot cycle, we can say that the heat gained by a gas during isothermal expansion is equal to the heat given off by the gas during isothermal compression. Thus, we can write the equation:

Q₁ = Q₂

where Q₁ - heat received by gas during isothermal expansion, Q₂ - heat given off by gas during isothermal compression.

It is also known that the efficiency of the Carnot cycle is 25%, which can be written as:

h = W_1-2/Q₁ = 0.25

where W_1-2 - work done by a gas during isothermal expansion.

Expressing the work W from the equation for efficiency_1-2, we get:

W_1-2 = 0.25 * Q₁

Substituting the heat value Q₁, we get:

W_1-2 = 0.25 * 240 J = 60 J

Thus, the work done by the gas during isothermal compression is also 60 J.

Description of the digital product: "Gas performing the Carnot cycle, the efficiency of which is 25%"

This digital product is a physics textbook dedicated to the Carnot cycle and the efficiency of gases. The manual examines in detail the theory of the Carnot cycle in terms of heat engines, calculates the efficiency of gases performing the Carnot cycle, and provides a detailed analysis of the results obtained.

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This product is a gas that undergoes the Carnot cycle and has an efficiency of 25%. The problem statement states that during isothermal expansion the gas produces 240 J of work.

The Carnot cycle is an ideal thermodynamic cycle consisting of two isothermal and two adiabatic processes. In the process of isothermal expansion of a gas, its volume increases at a constant temperature, and in the process of isothermal compression, its volume decreases at a constant temperature.

To solve the problem, it is necessary to find the work done by the gas under isothermal compression. To do this, you can use the formula for the work done by a gas during isothermal expansion:

W = nRT ln(V2/V1),

where W is the work done by the gas, n is the amount of substance in the gas, R is the universal gas constant, T is the temperature of the gas, V1 and V2 are the volumes of gas at the beginning and end of isothermal expansion, respectively.

To find work under isothermal compression, you can use the inverse formula:

W' = -nRT ln(V2'/V1'),

where W' is the work done by the gas during isothermal compression, V1' and V2' are the volumes of gas at the beginning and end of isothermal compression, respectively.

Thus, to solve the problem it is necessary to know the values ​​of gas volumes before and after isothermal expansion, as well as to know the amount of gas substance and temperature.

Additional information about the characteristics of this gas, such as its name, composition and other parameters, is not indicated in the problem statement, so they may be unknown.

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