Question

The specific heat at constant volume for a gas is 0.075 cal/g and at constant pressure is 0.125 cal/g. Calculate: (a) the molar mass of gas (b) atomicity of gas (c) no. of atoms, if gas in its 1 mole.

• A. $a\left)40b\right)1.66c)6.023\times {10}^{23}$
• B. $a\left)30b\right)0.66c)6.023\times {10}^{23}$
• C. $a\left)40b\right)1.66c)=5.023\times {10}^{22}$
• D. None of these

Answer 1

The correct option is A $a\left)40b\right)1.66c)6.023\times {10}^{23}$

Given,

Specific heats at constant P, $\left(C_p\right)=0.125cal/g$
Specific heats at constant V, $\left(C_v\right)=0.075cal/g$

(a) $\because C_p-C_v=\frac{R}{M}$

$\therefore 0.125-0.075=\frac{2}{M}$

or $M=40$

(b) For atomicity, $\gamma =\frac{C_p}{C_v}=\frac{0.125}{0.075}=1.66$

$i.e.,$ gas is monoatomic.

(c) Since gas is monoatomic and thus no. of atoms of gas in 1 mole,
$=6.023\times {10}^{23}atoms$

Hence, option A is correct.