Monatomic gas under pressure 0.3 MPa, iso

Monatomic gas expands isobarically from a volume of 2 to 7 dm³ at a pressure of 0.3 MPa.

It is necessary to determine:

1. work done by gas;
2. increase in internal energy;
3. amount of heat supplied.

To solve the problem you need to use the formulas:

• Work done by gas: A = pΔV, Where p - gas pressure, ΔV - change in gas volume.
• Internal energy increment: ΔU = Q - A, Where Q - amount of heat supplied.

Substituting the data from the condition, we get:

• A = 0.3 MPa × (7 dm³ - 2 dm³) = 1.5 J;
• ΔU = Q - A, therefore, Q = ΔU + А. To find ΔU, it is necessary to know the initial and final temperatures of the gas, which is not indicated in the problem statement.

Description of the digital product

Item name: Monatomic gas

Price: check on the website

Description:

The digital product "Monatomic Gas" is software for calculating the parameters of processes associated with the isochoric and isobaric expansion of a monatomic gas. With this product you can calculate the work done by the gas, the increment of internal energy and the amount of heat supplied under given conditions.

Specifications:

• Interface language: English
• System requirements: Windows 7 or higher, 64-bit processor
• File size: 10 MB

Downloading a digital product is possible after placing an order and payment on the website of the digital goods store.

A monatomic gas under a pressure of 0.3 MPa expands isobarically from a volume of 2 to 7 dm^3. To solve the problem, it is necessary to use the formula for calculating the work done by gas: A = pΔV, where p is the gas pressure, ΔV is the change in gas volume. Substituting the data from the condition, we get: A = 0.3 MPa × (7 dm^3 - 2 dm^3) = 1.5 J.

To calculate the increment in internal energy, it is necessary to know the initial and final temperatures of the gas, which is not indicated in the problem statement, so this value cannot be determined.

To calculate the amount of heat supplied, you can use the formula ΔU = Q - A, where Q is the amount of heat supplied. Substituting the resulting work value A = 1.5 J, we obtain: Q = ΔU + A. Since the value of ΔU is unknown, the amount of heat supplied Q is also impossible to determine.

However, to calculate these values, you can use the Monatomic Gas software, which allows you to calculate the parameters of the processes associated with the isochoric and isobaric expansion of a monatomic gas, including the work done by the gas, the increment of internal energy and the amount of heat supplied under given conditions.

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The described product is a monatomic gas, which is under a pressure of 0.3 MPa and expands isobarically from a volume of 2 to a volume of 7 dm^3. For this gas, it is necessary to determine the work done, the increment of internal energy and the amount of heat supplied.

To solve this problem, it is necessary to use the Guy-Lussac law, which states that in an isobaric process, the pressure of a gas is proportional to its temperature. It is also necessary to use the ideal gas equation of state, which relates the pressure, volume, temperature and amount of gas substance.

According to the assignment, the gas pressure is constant and equal to 0.3 MPa, so we can apply the formula for the work done by gas during an isobaric process:

A = p * ΔV,

where A is the work done by the gas, p is the gas pressure, ΔV is the change in gas volume.

Substituting the known values, we get:

A = 0.3 MPa * (7 dm^3 - 2 dm^3) = 1.5 MPa * dm^3.

Now it is necessary to determine the increment in the internal energy of the gas. According to the first law of thermodynamics, the increment in internal energy is equal to the difference between the perfect work of the gas and the amount of heat supplied:

ΔU = A - Q,

where ΔU is the increment of internal energy, Q is the amount of heat supplied.

According to the conditions of the problem, the gas is ideal, so you can use the ideal gas equation of state to determine the gas temperature before and after the process. Since the pressure is constant, the volume has increased, and the temperature of the gas has also increased. From the equation of state of an ideal gas it follows:

pV = nRT,

where n is the amount of gas substance, R is the universal gas constant.

Since the amount of substance in the gas remains unchanged, we can write:

p1V1/T1 = p2V2/T2,

where p1 and T1 are the pressure and temperature of the gas before the process, p2 and T2 are the pressure and temperature of the gas after the process.

Let's express T1 and T2:

T1 = p1V1/(nR),

T2 = p2V2/(nR).

Substituting the known values, we get:

T1 = 0.3 MPa * 2 dm^3/(nR),

T2 = 0.3 MPa * 7 dm^3/(nR).

The difference between T2 and T1 will be equal to the gas temperature increment:

ΔT = T2 - T1 = 0.3 MPa * (7 dm^3 - 2 dm^3)/(nR) - 0.3 MPa * 2 dm^3/(nR).

The amount of heat supplied can now be determined using the ideal gas equation of state and the equation for the change in internal energy. For an ideal gas the following relations hold:

ΔU = Cv * ΔT,

Q = ΔU + A,

where Cv is the molar heat capacity at constant volume.

The molar heat capacity at constant volume for a monatomic gas is 3/2 * R, so:

ΔU = 3/2 * nR * ΔT,

Q = ΔU + A = 3/2 * nR * ΔT + 1.5 MPa * dm^3.

Substituting the known values, we get:

ΔU = 3/2 * nR * [0.3 MPa * (7 dm^3 - 2 dm^3)/(nR) - 0.3 MPa * 2 dm^3/(nR)] = 3/2 * 0 .3 MPa * 5 dm^3 = 2.25 MPa * dm^3,

Q = ΔU + A = 2.25 MPa * dm^3 + 1.5 MPa * dm^3 = 3.75 MPa * dm^3.

Thus, the perfect work of the gas is 1.5 MPa * dm^3, the increment of internal energy is 2.25 MPa * dm^3, and the amount of heat supplied is 3.75 MPa * dm^3.

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2. Excellent quality and fast delivery.
3. The digital product is exactly as described.
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5. Fast and high-quality service, thank you!
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7. Excellent price-quality ratio.

Peculiarities:

It is very convenient that the digital product Monatomic gas can be purchased online, without having to leave your home.

A fast and convenient way to get the right gas, without queues and long waiting times.

The quality of the gas corresponds to the declared characteristics, which is important for its use in industrial processes.

The availability and convenience of payment through the online store make the purchase process as simple and convenient as possible.

Eliminating the need to manually fill out gas purchase paperwork saves time and reduces the chance of errors.

Fast delivery of gas to the place of use saves time and resources on its transportation.

The ability to order the right amount of gas allows you to optimize the cost of its purchase and use.

Clear information about the characteristics of the gas and its application allows you to choose the right product and use it safely.

The convenient interface of the online store and round-the-clock customer support make the process of buying gas as comfortable as possible.

The opportunity to receive discounts and special offers when buying a digital product Monatomic gas makes it even more attractive to buyers.