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0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas?
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0.75 kg of an ideal gas at 15C temperature is contained in a cylinder ...
To determine the density of the gas, we can use the ideal gas law equation, which states that the pressure (P) times the volume (V) is equal to the number of moles (n) times the gas constant (R) times the temperature (T):
PV = nRT
We are given the volume of the cylinder (V = 0.5 m^3) and the temperature before (T1 = 15°C = 15 + 273.15 = 288.15 K) and after (T2 = 150°C = 150 + 273.15 = 423.15 K) heating the gas. We are also given the mass of the gas (m = 0.75 kg). We need to find the density (ρ) of the gas.
Step 1: Calculate the number of moles (n)
We can use the equation n = m/M, where M is the molar mass of the gas. Since the gas is ideal, we can assume it follows the ideal gas law, which means its molar mass is equal to its molecular weight.
Step 2: Calculate the pressure (P)
Since the gas is heated at constant pressure, the pressure remains the same before and after heating. Therefore, we can assume the pressure is constant and use the initial pressure to calculate the density.
Step 3: Calculate the density (ρ)
The density is defined as the mass per unit volume. Therefore, we can calculate the density (ρ) by dividing the mass of the gas by the volume of the cylinder.
Now let's calculate each step in detail.
Step 1: Calculate the number of moles (n)
To calculate the number of moles, we need to know the molar mass of the gas. However, it is not provided in the question. Therefore, we cannot proceed with this calculation without knowing the molar mass of the gas.
Step 2: Calculate the pressure (P)
Since the gas is heated at constant pressure, we can assume the pressure remains the same before and after heating. Therefore, we can use the initial pressure to calculate the density.
Step 3: Calculate the density (ρ)
Density (ρ) is defined as mass (m) divided by volume (V). Therefore, we can calculate the density by dividing the mass of the gas by the volume of the cylinder.
Density (ρ) = mass (m) / volume (V)
Density (ρ) = 0.75 kg / 0.5 m^3
Density (ρ) = 1.5 kg/m^3
Therefore, the density of the gas is 1.5 kg/m^3.
PV = nRT
We are given the volume of the cylinder (V = 0.5 m^3) and the temperature before (T1 = 15°C = 15 + 273.15 = 288.15 K) and after (T2 = 150°C = 150 + 273.15 = 423.15 K) heating the gas. We are also given the mass of the gas (m = 0.75 kg). We need to find the density (ρ) of the gas.
Step 1: Calculate the number of moles (n)
We can use the equation n = m/M, where M is the molar mass of the gas. Since the gas is ideal, we can assume it follows the ideal gas law, which means its molar mass is equal to its molecular weight.
Step 2: Calculate the pressure (P)
Since the gas is heated at constant pressure, the pressure remains the same before and after heating. Therefore, we can assume the pressure is constant and use the initial pressure to calculate the density.
Step 3: Calculate the density (ρ)
The density is defined as the mass per unit volume. Therefore, we can calculate the density (ρ) by dividing the mass of the gas by the volume of the cylinder.
Now let's calculate each step in detail.
Step 1: Calculate the number of moles (n)
To calculate the number of moles, we need to know the molar mass of the gas. However, it is not provided in the question. Therefore, we cannot proceed with this calculation without knowing the molar mass of the gas.
Step 2: Calculate the pressure (P)
Since the gas is heated at constant pressure, we can assume the pressure remains the same before and after heating. Therefore, we can use the initial pressure to calculate the density.
Step 3: Calculate the density (ρ)
Density (ρ) is defined as mass (m) divided by volume (V). Therefore, we can calculate the density by dividing the mass of the gas by the volume of the cylinder.
Density (ρ) = mass (m) / volume (V)
Density (ρ) = 0.75 kg / 0.5 m^3
Density (ρ) = 1.5 kg/m^3
Therefore, the density of the gas is 1.5 kg/m^3.
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0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas?
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0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas?.
0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 0.75 kg of an ideal gas at 15C temperature is contained in a cylinder of 0.5metre cube capacity.the gas is heated at constant pressure until it attains a. Temperature of 150C.determine the density of the gas?.
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