Question

Идеальный газ 2 моля сжали изобарно, так что объём уменьшился в 3 раза.Определите работу газа, если начальная температура 77 градусов Цельсия.

Answer 1

Рассмотрим процесс в обратном направлении.
Q=-Ab;
Q=P*dV+0,5*j*(m/M)*R*dT;
 (m/M)*R*dT=P*dV;
Q=(1+0,5*j)*(m/M)*R*dT; 
dT=T-T1;
 V/T=V1/T1;
 T1=T*(V1/V);
 T1=T/3;
T=273+77=350;
Q=(1+0,5*3)*2*8,31*(350-350/3)=....

Answer 2

Calculation of Work Done by the Gas

To determine the work done by the gas, we can use the formula:

Work (W) = -PΔV

Where: - W is the work done by the gas - P is the pressure of the gas - ΔV is the change in volume of the gas

In this case, the gas is compressed isobarically, meaning the pressure remains constant. The volume is reduced to one-third of its initial value.

Let's calculate the work done by the gas step by step:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius - Adding 273.15 to convert to Kelvin: T1 = 350.15 K

2. Determine the initial volume (V1): - The volume is reduced to one-third of its initial value, so the final volume (V2) is V1/3. - Since we are given the number of moles (n) and the gas constant (R), we can use the ideal gas law to calculate the initial volume: - Ideal gas law: PV = nRT - Rearranging the equation to solve for V: V = (nRT)/P - Substituting the given values: - n = 2 moles - R = 8.314 J/(mol·K) (gas constant) - P = constant (since it is an isobaric process) - T = T1 (initial temperature) - Calculating V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's calculate the work done by the gas using the given information.

Calculation Steps:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77 degrees Celsius = 350.15 K

2. Determine the initial volume (V1): - Use the ideal gas law: V1 = (nRT1)/P - Given: - n = 2 moles - R = 8.314 J/(mol·K) - P = constant (since it is an isobaric process) - T1 = 350.15 K - Calculate V1 using the ideal gas law equation.

3. Calculate the final volume (V2): - V2 = V1/3

4. Calculate the change in volume (ΔV): - ΔV = V2 - V1

5. Calculate the work done by the gas (W): - W = -PΔV

Let's perform the calculations step by step.

Calculation:

1. Convert the initial temperature from Celsius to Kelvin: - Initial temperature (T1) = 77