Question

The specific heat of argon at constant volume is $0.075\text{kcal/kg K}$. Calculate its atomic weight [ $R=2\text{cal/mol K}$ ]

• A. $40\text{gram/mole}$
• B. $70\text{gram/mole}$
• C. $60\text{gram/mole}$
• D. $25\text{gram/mole}$

Answer 1

The correct option is A $40\text{gram/mole}$

Argon is a monoatomic gas $(n=3)$
its molar specific heat at constant volume will be,
$C_v=\frac{n}{2}R=\frac{3R}{2}$
$\Rightarrow C_v=\frac{3}{2}\times 2=3\text{cal / mol.K}$
Relation between molar specific heat and specific heat capacity is,
$C_v=M_{w}C$
$\because (C=0.075\text{k cal/kg.K,}{M}_w=\text{atomic weight}\text{)}$,
specific heat is always defined as per unit mass
$\Rightarrow 3\text{cal/mol.k}=M_w\times 0.075\text{cal/g.k}$
$\Rightarrow M_w=\frac{3}{0.075}=40\text{gram/mole}$