The amount of heat energy required to raise t | vedclass

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Question

(A) Since the volume of the gas remains constant,the heat energy required is given by $\Delta Q = n C_V \Delta T$.For Helium $(He)$,the molar mass is

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$\frac{3}{8}{N_a}{k_B}\left( {{T_2} - {T_1}} \right)$

Vedclass · Answer

(A) Since the volume of the gas remains constant,the heat energy required is given by $\Delta Q = n C_V \Delta T$.For Helium $(He)$,the molar mass is $4\, g/mol$. Therefore,the number of moles $n$ in $1\, g$ of Helium is $n = \frac{1}{4}$.Helium is a monatomic gas,so its molar heat capacity at constant volume is $C_V = \frac{3}{2} R$.Given the temperature change $\Delta T = T_2 - T_1$,we substitute these values into the formula:$\Delta Q = n C_V \Delta T = \left( \frac{1}{4} \right) \left( \frac{3}{2} R \right) (T_2 - T_1) = \frac{3}{8} R (T_2 - T_1)$.Using the relation $R = N_a k_B$,where $N_a$ is Avogadro's number and $k_B$ is the Boltzmann constant,we get:$\Delta Q = \frac{3}{8} N_a k_B (T_2 - T_1)$.

The amount of heat energy required to raise the temperature of $1\, g$ of Helium at $NTP$ from $T_1\, K$ to $T_2\, K$ is:

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