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The root mean square speed of 8 g of He is 300 ms–1. Total kinetic energy of He gas is:
- a)360 J
- b)240 J
- c)120 J
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Total Kinetic Energy of He Gas
Root Mean Square Speed of He Gas = 300 m/s
Mass of He Gas (m) = 8 g = 0.008 kg (as 1 g = 0.001 kg)
Boltzmann Constant (k) = 1.38 × 10^-23 J/K (given)
Using the formula for calculating Root Mean Square Speed,
vRMS = √(3kT/m)
where T is the temperature of the gas.
Rearranging the formula, we get
T = m*vRMS^2 / 3k
Substituting the given values, we get
T = (0.008 kg)*(300 m/s)^2 / (3*1.38 × 10^-23 J/K)
T = 2.603 × 10^5 K
Using the formula for calculating Total Kinetic Energy of a Gas,
KE = (3/2)*nRT
where n is the number of moles of gas, R is the gas constant, and T is the temperature of the gas.
Since we know the temperature and mass of He gas, we can calculate the number of moles using the formula
n = m/M
where M is the molar mass of He gas (4 g/mol).
Substituting the values, we get
n = 0.008 kg / 4 g/mol = 0.002 mol
Substituting the values of n, R, and T, we get
KE = (3/2)*(0.002 mol)*(8.314 J/mol·K)*(2.603 × 10^5 K)
KE = 119.9 J ≈ 120 J
Therefore, the total kinetic energy of He gas is 120 J (option A is correct).
Root Mean Square Speed of He Gas = 300 m/s
Mass of He Gas (m) = 8 g = 0.008 kg (as 1 g = 0.001 kg)
Boltzmann Constant (k) = 1.38 × 10^-23 J/K (given)
Using the formula for calculating Root Mean Square Speed,
vRMS = √(3kT/m)
where T is the temperature of the gas.
Rearranging the formula, we get
T = m*vRMS^2 / 3k
Substituting the given values, we get
T = (0.008 kg)*(300 m/s)^2 / (3*1.38 × 10^-23 J/K)
T = 2.603 × 10^5 K
Using the formula for calculating Total Kinetic Energy of a Gas,
KE = (3/2)*nRT
where n is the number of moles of gas, R is the gas constant, and T is the temperature of the gas.
Since we know the temperature and mass of He gas, we can calculate the number of moles using the formula
n = m/M
where M is the molar mass of He gas (4 g/mol).
Substituting the values, we get
n = 0.008 kg / 4 g/mol = 0.002 mol
Substituting the values of n, R, and T, we get
KE = (3/2)*(0.002 mol)*(8.314 J/mol·K)*(2.603 × 10^5 K)
KE = 119.9 J ≈ 120 J
Therefore, the total kinetic energy of He gas is 120 J (option A is correct).
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