The rms speed of the molecules in 1.9 g of hydrogen gas is 1800 m/s. What is the

Question

The rms speed of the molecules in 1.9 g of hydrogen gas is 1800 m/s. What is the total translational kinetic energy of the gas molecules? Express your answer to two significant figures and include the appropriate units. What is the thermal energy of the gas? Express your answer to two significant figures and include the appropriate units. 500 J of work are done to compress the gas while, in the same process, 1200 J of heat energy are transferred from the gas to the environment. Afterward. what is the rms speed of the molecules? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

[I could see that, you have correctly done parts A and B and need help with just part C, So I am solving for part C].

Part (C) Given that,

E( work done on the gas) = 500 J ; E(lost) = 1200 J ; m = 1.9 g = 0.0019 kg ;

E(thermal) = 5.1 kJ = 5100 J

The total energy that the molecule has is;

E(total) = E(thermal) + E(work done on gas) - E(lost to the environment)

E(toyal) = 5100 + 500 - 1200 = 4400 J

We know that, E = 1/2 m v2 Here, v = V(rms)

V(rms) = sqrt (2 E/m) = sqrt ( 2 x 4400 / 0.0019) = 2152 m/s

Hence, V(rms) = 21512 m/s

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