The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1 K to T2 K is:

  • Option 1)

    \frac{3}{4}\text{N}_{\text{a}} \text{k}_{\text{B}}\left ( \frac{\text{T}_{2}}{\text{T}_{1}} \right )

  • Option 2)

    \frac{3}{8}\text{N}_{\text{a}} \text{k}_{\text{B}}\left (\text{T}_{2}-\text{T}_{1} \right )

  • Option 3)

    \frac{3}{2}\text{N}_{\text{a}} \text{k}_{\text{B}}\left (\text{T}_{2}-\text{T}_{1} \right )

  • Option 4)

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

 

Answers (1)

As we learnt in

Heat (delta Q) -

It is the energy transferred between a system and its surrounding because of the temperature difference between them.

- wherein

Heat always flow from high temperature to low temperature.

 

 

 

1g of Helium is \frac{1}{4} mole of Helium 

n=\frac{1}{4}

Amount of heat energy required to raise the temperature = nC_{v}\Delta T

=\frac{1}{4}.(\frac{3R}{2}).(T_{2}-T_{1})=\frac{3}{8}R(T_{2-T_{1}})

\Delta Q=\frac{3}{8}.N_{a}K_{B}(T_{2}-T_{1})

Correct option is 2.


Option 1)

\frac{3}{4}\text{N}_{\text{a}} \text{k}_{\text{B}}\left ( \frac{\text{T}_{2}}{\text{T}_{1}} \right )

This option is incorrect 

Option 2)

\frac{3}{8}\text{N}_{\text{a}} \text{k}_{\text{B}}\left (\text{T}_{2}-\text{T}_{1} \right )

This option is correct 

Option 3)

\frac{3}{2}\text{N}_{\text{a}} \text{k}_{\text{B}}\left (\text{T}_{2}-\text{T}_{1} \right )

This option is incorrect 

Option 4)

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

This option is correct 

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