Question

An ideal gas is heated by 160 J at constant pressure It's temperature rises by 50° C and if 240 J of heat is supplied at constant volume temperature rises by 100° C then its degree of freedom should be ​

Answer 1

At constant pressure, the ideal gas is heated by 160 J.

• heat change in the system, $\sf{\Delta Q=160\ J}$

• rise in temperature, $\sf{\Delta T=50^oC}$

The heat change in the system at constant pressure is,

$\sf{\longrightarrow \Delta Q=C_P\Delta T}$

$\sf{\longrightarrow160=50C_P}$

$\sf{\longrightarrow C_P=3.2\ J\,K^{-1}}$

At constant volume, heat supplied is utilised to change its internal energy.

• change in internal energy, $\sf{\Delta u=240\ J}$

• rise in temperature, $\sf{\Delta T=100^oC}$

The change in internal energy is given by,

$\sf{\longrightarrow\Delta U=C_V\Delta T}$

$\sf{\longrightarrow240=100C_V}$

$\sf{\longrightarrow C_V=2.4\ J\,K^{-1}}$

Then, degree of freedom is given by,

$\sf{\longrightarrow 1+\dfrac{2}{f}=\dfrac{C_P}{C_V}}$

$\sf{\longrightarrow 1+\dfrac{2}{f}=\dfrac{3.2}{2.4}}$

$\sf{\longrightarrow 1+\dfrac{2}{f}=\dfrac{4}{3}}$

$\sf{\longrightarrow\dfrac{2}{f}=\dfrac{1}{3}}$

$\sf{\longrightarrow\underline{\underline{f=6}}}$