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  4. A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0° C will be: (Given gas constant R =8.3 JK -1- moI -1 )

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Q. A cylinder of fixed capacity of $44.8$ litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by $20.0^{\circ} C$ will be : (Given gas constant $R =8.3\, JK ^{-1}- moI ^{-1}$ )

JEE MainJEE Main 2022Kinetic Theory

Solution:

No of moles $=\frac{44.8}{22.4}=2$
Gas is mono atomic so $C _{ v }=\frac{3}{2} R$
$\Delta Q = nC _{ v } \Delta T $
$=2 \times \frac{3}{2} R (20) $
$=60 \,R$
$=60 \times 8.3 $
$=498\, J$