Calculate the temperature (K) of N2 gas if the molecules have a speed of 818.049 m/s

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From the question we are told

Calculate the temperature (K) of N2 gas if the molecules have a speed of 818.049 m/s

Generally the equation for the root means square of the velocity    is mathematically given as

T=751K

Therefore

the temperature (K) of N2 gas if the molecules have a speed of 818.049 m/s

T=751K

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751.20K

Explanation:

To calculate the temperature of N2 gas, the following formula is used:

V(rms) = √3RT/mm

Where;

V(rms) = root means square of the velocity (818.049m/s)

R = gas law constant (8.3145J/Kmol)

T = temperature (K)

M = molar mass (kg/mol)

Molar mass of N2 = 14 + 14 = 28g/mol

Convert to kg/mol, we have;

28/1000 = 0.028kg/mol

V(rms) = √3RT/mm

818.049 = √3(8.3145 × T)/0.028

818.049 = √3(8.3145T)/0.028

818.049 = √24.9435T/0.028

818.049 = √890.839

818.049² = √890.839T²

669204.1666 = 890.839T

T = 669204.1666/890.839

T = 751.20K

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