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 .............. $J$(Given gas constant $R =8.3 \,JK ^{-1}- moI ^{-1}$ )
A$249$
B$415$
C$498$
D$830$
JEE MAIN 2022, Medium
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C$498$
c No of moles $=\frac{44.8}{22.4}=2$
Gas is mono atomic so $C _{ V }=\frac{3}{2} R$
$\Delta Q = nC _{ v } \Delta T$
$=2 \times \frac{3}{2} R (20)$
$=60 R$
$=60 \times 8.3$
$=498 \,J$
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