Question

При адиабатическом сжатии температура одноатомного газа возросла на 2 К. Определите массу газа, если при сжатии была совершена работа 1000 Дж. Молярная масса 4 г/моль. Ответ запишите в граммах.

Answer 1

Брат 2 дня назад эту же задачу выкладывал так никто и не решил :D (Danya)

Answer 2

Adiabatic Compression of a Monoatomic Gas

When a monoatomic gas undergoes adiabatic compression, its temperature increases. In this case, the temperature of the gas increased by 2 K. We are given that the work done during compression is 1000 J, and the molar mass of the gas is 4 g/mol. We need to determine the mass of the gas in grams.

To solve this problem, we can use the ideal gas law and the first law of thermodynamics. The ideal gas law states that:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of the gas - R is the ideal gas constant - T is the temperature of the gas

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:

ΔU = Q - W

Where: - ΔU is the change in internal energy - Q is the heat added to the system - W is the work done by the system

In this case, since the process is adiabatic (no heat exchange), the change in internal energy is equal to the work done:

ΔU = W

Therefore, we can write:

W = nCvΔT

Where: - W is the work done - n is the number of moles of the gas - Cv is the molar specific heat at constant volume - ΔT is the change in temperature

The molar specific heat at constant volume for a monoatomic gas is given by:

Cv = (3/2)R

Substituting the values given in the problem, we have:

1000 J = n(3/2)R(2 K)

Now, we can solve for the number of moles of the gas:

n = (1000 J) / [(3/2)R(2 K)]

The ideal gas constant R is approximately 8.314 J/(mol·K). Substituting this value, we get:

n ≈ (1000 J) / [(3/2)(8.314 J/(mol·K))(2 K)]

Simplifying the expression:

n ≈ (1000 J) / (24.942 J/(mol·K))

n ≈ 40.06 mol

Finally, to determine the mass of the gas in grams, we multiply the number of moles by the molar mass:

Mass = n × Molar Mass

Mass ≈ 40.06 mol × 4 g/mol

Mass ≈ 160.24 g

Therefore, the mass of the gas is approximately 160.24 grams.