Kinetic Theory Of Gases Question 79

Question: The amount of heat energy required to raise the temperature 1g of Helium at NTP, from T,K to

Options:

A) $ \frac{3}{2}N _{a}k _{B}( T _{2}-T _{1} ) $

B) $ \frac{3}{4}N _{a}k _{B}( T _{2}-T _{1} ) $

C) $ \frac{3}{4}N _{a}k _{B}\frac{T _{2}}{T _{1}} $

D) $ \frac{3}{8}N _{a}k _{B}( T _{2}-T _{1} ) $

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Answer:

Correct Answer: D

Solution:

[d] From first law of thermodynamics $ \Delta Q=\Delta U+\Delta W=\frac{3}{2}.\frac{1}{4}R( T _{2}-T _{1} )+0 $

$ =\frac{3}{8}N _{a}K _{B}(T _{2}-T _{1})[ \because K=\frac{R}{N} ] $