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  • Half mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume constant (heat capacity of the gas <img alt="\mathrm{=3 \m

Half mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume constant (heat capacity of the gas \mathrm{=3 \mathrm{~J} / \mathrm{g} \mathrm{K}} ) is
 

Option: 1

3276 \mathrm{~J}
 


Option: 2

1638 \mathrm{~J}


Option: 3

819 \mathrm{~J}


Option: 4

409.5 \mathrm{~J}


Answers (1)

best_answer

\mathrm{Q}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{n}\left(\mathrm{MC}_{\mathrm{v}}\right) \Delta \mathrm{T}

Here, volume is constant

Thus, \mathrm{\frac{P_1}{T_1}=\frac{P_2}{T_2} \Rightarrow T_2=2 T_1 \quad\left(\frac{P_2}{P_1}=2\right)}

Now, \mathrm{\Delta \mathrm{T}=\mathrm{T}_2-\mathrm{T}_1=2 \mathrm{~T}_1-\mathrm{T}_1=273 \mathrm{~K}}

So, \mathrm{Q=\frac{1}{2} \times 4 \times 3 \times 273=1638 \mathrm{~J}}

Posted by

rishi.raj

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