Question

The specific heat of a monatomic gas at constant volume is $0.075kcalk{g}^{-1}{K}^{-1}$. Its atomic weight will be

• A. $10$
• B. $30$
• C. $40$
• D. $90$

Answer 1

The correct option is C $40$

$C_v$ for a monoatomic gas at constant volume is $\frac{3R}{2}\approx 3cal-mo{l}^{-1}{K}^{-1}$
Let the atomic weight of the gas be $w$
$\therefore w$ grams of the gas requires the $3cal$ of heat to raise its temperature by $1K$.
$\therefore$ 1 gram of gas will require $\frac{3}{w}cal$ of heat to raise its temperature by $1K$.
$\therefore$ 1 kg of gas will require $\frac{3}{w}kcal$ of heat to raise its temperature by $1K$.
In the question, the above quantity is given to be $0.075kcalk{g}^{-1}{K}^{-1}$
$\therefore \frac{3}{w}=0.075$
Solving this, we get $w=40$