Determine the speed of departure of a piston weighing 4 kg from the cylinders

Solution to problem 20427: Given: piston mass - 4 kg, adiabatic coefficient - 40, initial pressure - 10^7 Pa, initial volume - 0.28 l. It is required to determine the speed of departure of the piston from the cylinder during the adiabatic expansion of hydrogen by a factor of 40.

Solution: We use Gay-Lussac's law for the adiabatic process: pV^k = const, where p is the gas pressure, V is its volume, k is the adiabatic coefficient.

The final volume of gas can be found through the initial volume and expansion coefficient: V2 = V1 * k,

where V1 is the initial volume of gas.

You can also use the ideal gas law: pV = nRT, where p is the gas pressure, V is its volume, n is the amount of gas substance, R is the universal gas constant, T is the gas temperature.

Considering that the process is adiabatic, then pV^k = const = p2V2^k.

We substitute the values ​​and find the pressure after expansion: p2 = p1 * (V1/V2)^k = 10^7 * (0.28/(0.28*40))^40 = 1.58 * 10^-5 Pa.

Next, we use the law of conservation of energy: (mv^2)/2 = (k/(k-1)) * p1 * V1 * ((V2/V1)^((k-1)/k) - 1), where m is the mass of the piston, v is its speed.

We substitute the values ​​and find the piston speed: v = sqrt((2 * k * p1 * V1)/(m * (k-1)) * ((V2/V1)^((k-1)/k) - 1) ) = 197.2 m/s.

Answer: the speed of departure of the piston from the cylinder during the adiabatic expansion of hydrogen by a factor of 40 is 197.2 m/s.

If you have any questions about the solution, please write. I will try to help.

Determination of the speed of departure of a piston weighing 4 kg from a cylinder

Solution tasks 20427

This digital product is a detailed solution to problem 20427 in physics, which is to determine the speed of departure of a piston weighing 4 kg from a cylinder during the adiabatic expansion of hydrogen by a factor of 40, if the initial pressure is 10^7 Pa and the initial volume is 0.28 liters.

The solution includes a brief statement of the problem, formulas and laws used in the solution, the derivation of the calculation formula and the answer. All material is presented in a clear and easily understandable form.

This digital product will be useful to students and teachers studying physics, as well as anyone interested in this science.

This digital product is a detailed solution to problem 20427 in physics, which is to determine the speed of departure of a piston weighing 4 kg from a cylinder during the adiabatic expansion of hydrogen by a factor of 40, if the initial pressure is 10^7 Pa and the initial volume is 0.28 liters.

The solution to the problem includes a brief statement of the problem, formulas and laws used in the solution, derivation of the calculation formula and the answer. All material is presented in a clear and easily understandable form.

To solve the problem, Gay-Lussac's law for an adiabatic process and the ideal gas law are used. Given that the process is adiabatic, the pressure after expansion is found and then the law of conservation of energy is used to determine the speed of the piston.

This digital product will be useful to students and teachers studying physics, as well as anyone interested in this science. If you have any questions about solving the problem, please contact me, I will try to help.

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This product is a detailed solution to problem 20427, which is to determine the speed of departure of a piston weighing 4 kg from a cylinder during the adiabatic expansion of hydrogen by a factor of 40.

From the problem conditions it is known that the initial pressure is 10^7 Pa, and the initial volume is 0.28 liters. It is also necessary to take into account that the mass of the piston is 4 kg.

To solve the problem, the laws of thermodynamics are applied, namely, the first law of thermodynamics and Gay-Lussac's law. Using these laws, it is possible to obtain a calculation formula for determining the piston ejection speed.

A detailed solution to a problem includes recording the conditions, formulas and laws used in the solution, derivation of the calculation formula and the answer. If you have any questions about the solution, the seller is ready to help and answer them.

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