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  4. If R is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from 273 K to 373 K when no work is done is

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Q. If $R$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273\, K$ to $373\, K$ when no work is done is

Thermodynamics

Solution:

As no work is done, therefore, $ΔW = 0$ According to first law of thermodynamics
$ΔQ = ΔU + ΔW = ΔU = nC_{V}ΔT=n\left(\frac{R}{\gamma-1}\right)\Delta T$
Here, $n =2, \gamma=\frac{5}{3}$
$\Delta T=T_{2}-T_{1}=\left(373-273\right)=100\,K$
$\Delta Q=2\times\frac{R}{\left(\frac{5}{3}-1\right)}\times100=300\,R$