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  • The internal energy of 3 moles of hydrogen at temperature T is equal to the internal energy of n moles of helium at temperature <img alt="\mathrm{T / 2}" src="https://entrancecorner.oncodecogs.com/

The internal energy of 3 moles of hydrogen at temperature T is equal to the internal energy of n moles of helium at temperature \mathrm{T / 2} The value of n is (assume hydrogen and helium to behave like ideal gases)

Option: 1

5


Option: 2

10


Option: 3

\frac{3}{2}


Option: 4

6


Answers (1)

best_answer

The internal energy of n moles of an ideal gas at temperature T is given by

\mathrm{U=\frac{f}{2} n R T}

Where f= number of degrees of freedom
For hydrogen, f = 5. Therefore

\mathrm{U_1=\frac{5}{2} \times 3 \times R T=\frac{15}{2} R T}

For helium, f = 3. Therefore

\mathrm{U_2=\frac{3}{2} n R(T / 2)=\frac{3}{4} n R T}

\mathrm{\text { Given } U_1=U_2 \text {, i.e. }}

\mathrm{\frac{15}{2} R T=\frac{3}{4} n R T}

Which gives n = 10

Posted by

Pankaj

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