2. A gas cylinder contains 1.0 g of hydrogen molecules. The...

2. A gas cylinder contains 1.0 g of hydrogen molecules. The rms speed of the molecules is 1800 m/s. (a) Determine the total translational energy of the gas molecules. (b) Find the thermal energy of the gas. (c) 500 J of work are done to compress the gas while, in the same process, 1200 J of heat are transferred from the gas to the environment. Determine the resulting rms speed of the gas molecules.

Transcript

00:01 High students in this question, a hydrogen gas is being given whose mass is taken as m to be equal to 1 .2 dam.

00:07 On the other hand, its vrms value is taken to be 1 ,600 meter per second.

00:13 Now in the first part of the question, we are asked to find out the value of translational kinetic energy, ke, which can be found out using the equation, ke to be equal to 1 by 2 into m into vrm square.

00:26 Now by substituting the values, our equation changes as k k -e to be equal to 1 by 2 into 1 .2 into 10 raise to minus 3 into 1 ,600 square, which on simplification gives the value of translational kinetic energy, k -e to be equal to 1 .536 kilo -jou.

00:46 Now in the second part of the question, we are asked to find out the value of thermal energy e, and we know that the equation of kinetic energy k -e is taken to be 1 by 2 into m into v.

00:59 Square where the value of v rm s is taken to be square root the value of 3 into r t divided by m where this t corresponds to the temperature r corresponds the universal gas constant and capital m corresponds to the monormus now by substituting the value of v rmns in the above equation we get the equation of kinetic energy to be equal to 1 by 2 into m into a value of 3 r t divided by capital letter m and here it should be noted that the number of moles of this particular hydrogen gas can be found out using the equation small letter n to be equal to given mass small letter m divided by the molar mass capital letter m from which we get the value of molar mass m to be equal to given mass m divided by number of moles n and here by substituting the value of this equation in the above equation of kinetic energy we get the value of kinetic energy k -e to be equal to 3 by 2 into nr t.

01:59 Now here the equation of thermal energy is taken as e to be equal to 5 divided by 2 into n into r t.

02:08 Now here by multiplying a quantity of 3 by 3 on the right -hand side of this equation, we get the thermal energy e to be equal to 5 divided by 3 into 3 nr -t divided by 2, which on simplification gives the value of thermal energy e to be equal to 5 divided by 3 into kinetic energy k.

02:30 Now by substituting the values, we get thermal energy e to be equal to 5 divided by 3 into 1 .536, which on simplification gives the value of thermal energy e to be equal to 2 .56 kilojou...

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