Specific Heat Of A Gas - Practice Questions & MCQ

Specific heat - The specific heat is the amount of heat per unit mass required to raise the temperature by one Kelvin.

Now for gases we have several types of specific heat, but here we will discuss basically two types of specific heat - 

1. 1. Specific heat at constant volume $\left(\mathbf{c}_{\mathrm{v}}\right)$-lt is defined as the quantity of heat required to raise the temperature of unit mass of gas through $1^{\circ} \mathrm{C}$ or 1 Kelvin at constant volume.

   It is given as -

   $
   c_v=\frac{(\Delta Q)_V}{m \Delta T}
   $

   
   If 1 mole of gas is placed at the place of unit mass is considered, then this specific heat of gas is called molar specific heat at constant volume and is represented by $\mathbf{C v}$ (Here C is capital)

   So, for molar specific heat -

   $
   C_V=M c_V=\frac{M(\Delta Q)_V}{m \Delta T}=\frac{1}{\mu} \frac{(\Delta Q)_V}{\Delta T} \quad\left[\text { As } \mu=\frac{m}{M}\right]
   $

   2. Specific heat at constant pressure ( $\mathbf{c}_{\mathrm{p}}$ ) - It is defined as the quantity of heat required to raise the temperature of unit mass of gas through $1^{\circ} \mathrm{C}$ or 1 Kelvin at constant pressure.

   It is given as - $c_p=\frac{(\Delta Q)_p}{m \Delta T}$
   If 1 mole of gas is placed at the place of unit mass is considered, then this specific heat of gas is called molar specific heat at constant pressure and is represented by $\mathbf{C}_{\mathrm{p}}$ (Here C is capital)

So, for molar specific heat at constant pressure - 

                                 $C_p=M c_p=\frac{M(\Delta Q)_p}{m \Delta T}=\frac{1}{\mu} \frac{(\Delta Q)_p}{\Delta T} \quad\left[\right.$ As $\left.\mu=\frac{m}{M}\right]$