A cylinder of fixed capacity of 44.8 , L cont | vedclass

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Question

(C) The number of moles $n$ of the gas at $STP$ is given by the volume divided by the molar volume at $STP$ $(22.4 \, L/mol)$:$n = \frac{44.8 \, L}{22

Vedclass · Accepted Answer

$498$

Vedclass · Answer

(C) The number of moles $n$ of the gas at $STP$ is given by the volume divided by the molar volume at $STP$ $(22.4 \, L/mol)$:$n = \frac{44.8 \, L}{22.4 \, L/mol} = 2 \, mol$.Since helium is a monoatomic gas,its molar heat capacity at constant volume is $C_V = \frac{3}{2} R$.The heat required to raise the temperature by $\Delta T = 20.0^{\circ} C$ (which is equivalent to $20.0 \, K$) is given by the formula:$\Delta Q = n C_V \Delta T$.Substituting the values:$\Delta Q = 2 	imes (\frac{3}{2} R) 	imes 20.0$$\Delta Q = 3 	imes R 	imes 20.0 = 60 R$.Given $R = 8.3 \, J \, K^{-1} \, mol^{-1}$:$\Delta Q = 60 	imes 8.3 = 498 \, J$.

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

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