Previous Year NEET Question- Kinetic Theory L-9

Question: One mole of an ideal gas requires $207 \mathrm{~J}$ heat to rise the temperature by $10 \mathrm{~K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{~K}$, the heat required is (Given the gas constant $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ ) [CBSE AIPMT 1990]#

A) $198.7 \mathrm{~J}$

B) $29 \mathrm{~J}$

C) $215.3 \mathrm{~J}$

D) $124 \mathrm{~J}$

Answer: $124 \mathrm{~J}$#

Solution:#

Molar specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram mole of the substance through a unit degree. As $(d Q)_p=\mu C_p d T$ (At constant pressure) and $(d O)_V=\mu C_V d T$ (At constant volume) Given, $(d Q)_p=207 \mathrm{~J}$ $$ \begin{aligned} R & =8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \ d T & =10 \mathrm{~K} \end{aligned} $$

Putting value in Eq. (i) $$ \begin{array}{rlrl} & 207=1 \times C_p \times 10 \ \therefore \quad C_p=20.7 \mathrm{~J} / \mathrm{kg} \ \text { As } \quad C_p-C_V & =R=8.3 \ & C_V & =20.7-8.3=12.4 \mathrm{~J} \ \therefore \quad(d Q)_V & =1 \times 12.4 \times 10 \ & = & 124 \mathrm{~J} \end{array} $$