Question

В баллоне находится газ массой 2,5 кг при температуре 27 °C и давлении 5×105 Па. Когда часть газа была выпущена, а оставшаяся часть нагрета до 177 °С, давление возросло до 6×105 Па. Какова плотность оставшейся части газа, если объем баллона 1м?

Answer 1

Ответ:

2кг/м3

Объяснение:

P1*V=m1*RT1/M это идеальный газ

P2*V=m2*R*T2/M

m1/m2=P1*T2/P2*T1

m2=m1T1P2/P1T2=2кг

p=m2/v=2/1=2кг/м3

Answer 2

Calculation of Density of the Remaining Gas

To calculate the density of the remaining 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 gas - R is the ideal gas constant - T is the temperature of the gas

We are given the following information: - Mass of the gas = 2.5 kg - Temperature before releasing a part of the gas = 27 °C = 300 K - Pressure before releasing a part of the gas = 5 × 10^5 Pa - Temperature after releasing a part of the gas = 177 °C = 450 K - Pressure after releasing a part of the gas = 6 × 10^5 Pa - Volume of the balloon = 1 m^3

To find the density of the remaining gas, we need to calculate the number of moles of gas using the ideal gas law equation and then divide the mass of the gas by the volume of the balloon.

Let's calculate the number of moles of gas before and after releasing a part of it.

1. Calculation before releasing a part of the gas:

Using the ideal gas law equation, we can rearrange it to solve for the number of moles (n):

n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

We can calculate the number of moles (n) using the above equation.

2. Calculation after releasing a part of the gas:

Using the ideal gas law equation again, we can calculate the number of moles (n) after releasing a part of the gas. The pressure and temperature have changed, so we need to use the new values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

We can calculate the number of moles (n) using the above equation.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by step.

Calculation Steps:

1. Calculation of the number of moles of gas before releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

We can calculate the number of moles (n) using the above equation.

2. Calculation of the number of moles of gas after releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

We can calculate the number of moles (n) using the above equation.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by step.

Calculation:

1. Calculation of the number of moles of gas before releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

Using the above equation, we can calculate the number of moles (n) of the gas before releasing a part of it.

2. Calculation of the number of moles of gas after releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

Using the above equation, we can calculate the number of moles (n) of the gas after releasing a part of it.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by step.

Calculation:

1. Calculation of the number of moles of gas before releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

Using the above equation, we can calculate the number of moles (n) of the gas before releasing a part of it.

2. Calculation of the number of moles of gas after releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

Using the above equation, we can calculate the number of moles (n) of the gas after releasing a part of it.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by step.

Calculation:

1. Calculation of the number of moles of gas before releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

Using the above equation, we can calculate the number of moles (n) of the gas before releasing a part of it.

2. Calculation of the number of moles of gas after releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

Using the above equation, we can calculate the number of moles (n) of the gas after releasing a part of it.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by step.

Calculation:

1. Calculation of the number of moles of gas before releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

Using the above equation, we can calculate the number of moles (n) of the gas before releasing a part of it.

2. Calculation of the number of moles of gas after releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

Using the above equation, we can calculate the number of moles (n) of the gas after releasing a part of it.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by step.

Calculation:

1. Calculation of the number of moles of gas before releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 5 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 300 K

Using the above equation, we can calculate the number of moles (n) of the gas before releasing a part of it.

2. Calculation of the number of moles of gas after releasing a part of it:

Using the ideal gas law equation: n = PV / RT

Substituting the given values: - P = 6 × 10^5 Pa - V = 1 m^3 - R = 8.314 J/(mol·K) - T = 450 K

Using the above equation, we can calculate the number of moles (n) of the gas after releasing a part of it.

3. Calculation of the density of the remaining gas:

To find the density of the remaining gas, we divide the mass of the gas by the volume of the balloon.

Now, let's perform the calculations step by