Question

Газ массой m = 200 г нагревают на ΔТ = 60°С один раз при постоянном давлении, а другой раз при постоянном объеме. Оказалось, что при постоянном давлении требуется подвести на 1 кДж больше тепла, чем при постоянном объеме. Найдте среднюю молярную массу газа, считая его идеальным.

Answer 1

Давление постоянно (p-const)
Q1=(m/M)*Cv*ΔT+m/M*R*ΔT

Объем постоянный (V-const)
Q2=(m/M)*Cv*ΔT

ΔQ = Q1-Q2 = (m/M)*R*ΔT

Находим:
M = m*R*ΔT/ΔQ

Подставляем данные:
M = 0,200*8,31*60/1000 ≈ 0,100 кг/моль  или 100 г/моль

Answer 2

Calculation of the Average Molar Mass of the Gas

To find the average molar mass of the gas, we can use the ideal gas law equation:

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

In this case, we have two scenarios: one where the gas is heated at constant pressure and another where it is heated at constant volume. Let's analyze each scenario separately.

Heating at Constant Pressure

When the gas is heated at constant pressure, the equation becomes:

PΔV = nRΔT

Since the pressure is constant, ΔP = 0, and therefore ΔV = V.

VΔP = nRΔT

We are given that ΔT = 60°C and ΔQ = 1 kJ (1000 J).

VΔP = nRΔT = ΔQ

Now, we can rearrange the equation to solve for n, the number of moles of the gas:

n = (VΔP) / (RΔT)

Heating at Constant Volume

When the gas is heated at constant volume, the equation becomes:

ΔQ = nCvΔT

We are given that ΔT = 60°C and ΔQ = 1 kJ (1000 J).

ΔQ = nCvΔT = ΔQ

Now, we can rearrange the equation to solve for n, the number of moles of the gas:

n = ΔQ / (CvΔT)

Calculation of the Average Molar Mass

To find the average molar mass of the gas, we need to calculate the number of moles of the gas in each scenario and then take the average.

Let's assume the molar mass of the gas is M.

For the constant pressure scenario:

n1 = (VΔP) / (RΔT)

For the constant volume scenario:

n2 = ΔQ / (CvΔT)

The average molar mass can be calculated as:

M_avg = (n1M + n2M) / (n1 + n2)

Now, let's substitute the given values and calculate the average molar mass.

Calculation

Given: - m = 200 g (mass of the gas) - ΔT = 60°C (change in temperature) - ΔQ = 1 kJ (change in heat) - R = 8.314 J/(mol·K) (ideal gas constant)

We need to find the average molar mass M_avg.

Using the equations derived above, we can calculate the number of moles of the gas in each scenario:

For the constant pressure scenario:

n1 = (VΔP) / (RΔT)

For the constant volume scenario:

n2 = ΔQ / (CvΔT)

Finally, we can calculate the average molar mass:

M_avg = (n1M + n2M) / (n1 + n2)

Let's perform the calculations.

Calculation Steps

1. Convert the mass of the gas from grams to kilograms: - m = 200 g = 0.2 kg

2. Calculate the number of moles of the gas in each scenario: - For the constant pressure scenario: - n1 = (VΔP) / (RΔT) - For the constant volume scenario: - n2 = ΔQ / (CvΔT)

3. Calculate the average molar mass: - M_avg = (n1M + n2M) / (n1 + n2)

Let's perform the calculations.