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If the root mean square speed of an argon gas atom at temperature T is equal to the average speed of a helium gas atom at -20 °C, then T will be:
Given:- atomic mass of Ar = 39.9 u
Atomic mass of He = 4.0 u
- a)2523.7 K
- b)2523.7 °C
- c)6729.8 K
- d)6729.8 °C
Correct answer is option 'A'. Can you explain this answer?
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If the root mean square speed of an argon gas atom at temperature T is...
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If the root mean square speed of an argon gas atom at temperature T is...
The root mean square speed of a gas atom is given by the equation:
v(rms) = √(3kT/m)
where v(rms) is the root mean square speed, k is the Boltzmann constant, T is the temperature, and m is the mass of the gas atom.
Assuming the average speed of a helium gas atom at -20°C is equal to the root mean square speed of an argon gas atom at temperature T, we can equate the two expressions:
v(average helium at -20°C) = v(rms argon at T)
Since the temperature of helium gas is -20°C (-20 + 273.15 = 253.15 K), we can substitute the values into the equation:
v(average helium at 253.15 K) = √(3kT/m)
Now, we need to find the temperature T at which the root mean square speed of an argon gas atom is equal to the average speed of a helium gas atom at -20°C. This requires rearranging the equation:
T = (v(average helium at 253.15 K))^2 * m / (3k)
Given the average speed of a helium gas atom at -20°C, the mass of a helium atom (4 atomic mass units), and the Boltzmann constant (1.380649 × 10^-23 J/K), we can substitute the values into the equation to find the temperature T.
v(rms) = √(3kT/m)
where v(rms) is the root mean square speed, k is the Boltzmann constant, T is the temperature, and m is the mass of the gas atom.
Assuming the average speed of a helium gas atom at -20°C is equal to the root mean square speed of an argon gas atom at temperature T, we can equate the two expressions:
v(average helium at -20°C) = v(rms argon at T)
Since the temperature of helium gas is -20°C (-20 + 273.15 = 253.15 K), we can substitute the values into the equation:
v(average helium at 253.15 K) = √(3kT/m)
Now, we need to find the temperature T at which the root mean square speed of an argon gas atom is equal to the average speed of a helium gas atom at -20°C. This requires rearranging the equation:
T = (v(average helium at 253.15 K))^2 * m / (3k)
Given the average speed of a helium gas atom at -20°C, the mass of a helium atom (4 atomic mass units), and the Boltzmann constant (1.380649 × 10^-23 J/K), we can substitute the values into the equation to find the temperature T.
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If the root mean square speed of an argon gas atom at temperature T is...
But question demands that r.m.s of argon = average speed of a helium .
so the solution is incorrect .
so the solution is incorrect .
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If the root mean square speed of an argon gas atom at temperature T is equal to the averagespeed of a helium gas atom at -20 °C, then T will be:Given:- atomic mass of Ar = 39.9 uAtomic mass of He = 4.0 ua)2523.7 Kb)2523.7°Cc)6729.8 Kd)6729.8 °CCorrect answer is option 'A'. Can you explain this answer?
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