Question

При адиабатическом расширении идеального одиоатомного газа в количестве 2 моль его температура изменилась на 10 К. Какую работу совершил газ ?

Answer 1

I=3    v=2 моль   ΔT=10 K     A=?
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A=(i/2)*v*R*ΔT=(3/2)*2*8.31*10=249.3 Дж
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Answer 2

Adiabatic Expansion of an Ideal Monoatomic Gas

When an ideal monoatomic gas undergoes adiabatic expansion, its temperature changes without any heat exchange with the surroundings. In this case, we have a quantity of 2 moles of the gas, and its temperature changes by 10 K. We need to calculate the work done by the gas during this process.

To calculate the work done during adiabatic expansion, we can use the formula:

W = (Cv / (γ - 1)) * (T2 - T1)

Where: - W is the work done by the gas - Cv is the molar specific heat capacity at constant volume - γ is the adiabatic index (also known as the heat capacity ratio or ratio of specific heats) - T2 is the final temperature - T1 is the initial temperature

To find the values for Cv and γ for an ideal monoatomic gas, we can refer to the search results.

According to source the molar specific heat capacity at constant volume (Cv) for an ideal monoatomic gas is approximately 12.5 J/(mol·K).

According to source the adiabatic index (γ) for an ideal monoatomic gas is approximately 5/3 or 1.67.

Now we can substitute the values into the formula to calculate the work done by the gas:

W = (12.5 / (1.67 - 1)) * (10)

Calculating this expression, we find:

W ≈ 75 J

Therefore, the gas has done approximately 75 Joules of work during the adiabatic expansion.

Please note that the values used in this calculation are approximate and may vary depending on the specific properties of the gas.