Question

One $\text{mole}$ of an ideal monoatomic gas is initially at $500\text{K}$. If $300\text{J}$ of heat is added at constant volume, the final temperature of the gas is
(Assume $R=8\text{J/mol K}$)

• A. $525\text{K}$
• B. $550\text{K}$
• C. $600\text{K}$
• D. $625\text{K}$

Answer 1

The correct option is A $525\text{K}$

Given, that gas is monoatomic
No. of moles of the gas $\left(n\right)=1$
Heat supplied $\left(Q\right)=200\text{J}$
Initial temperature $\left(T_i\right)=500\text{K}$
For monoatomic gas, $C_V=\frac{3R}{2}$

Since volume is constant, work done is zero.
From First law of thermodynamics, we know that
$\Delta Q=\Delta U+W$
$W=0\Rightarrow \Delta Q=\Delta U$
$\Rightarrow \Delta Q=\Delta U=n{C}_V\Delta T$
$\Rightarrow \Delta Q=\frac{3R}{2}\times (T_f-T_i)$
$\Rightarrow 300=\frac{3}{2}\times 8(T_f-500)$
$\Rightarrow T_f=525\text{K}$ is the final temperature.