CBSE-XI-Physics
27: Specific Heat Capacities of Gases
- #9Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?Ans : For two states to be connected by an isothermal process,
`` {P}_{1}{V}_{1}={P}_{2}{V}_{2}`` ...(i)
For the same two states to be connected by an adiabatic process,
`` {P}_{1}{{V}_{1}}^{\gamma }={P}_{2}{{V}_{2}}^{\gamma }`` ...(ii)
If both the equations hold simultaneously then, on dividing eqaution (ii) by (i) we get
`` {{V}_{1}}^{\gamma -1}={{V}_{2}}^{\gamma -1}``
Let the gas be monatomic. Then,
`` \gamma =\frac{5}{3}``
`` \Rightarrow {{V}_{1}}^{\frac{2}{3}}={{V}_{2}}^{\frac{2}{3}}``
`` \Rightarrow {V}_{1}={V}_{2}``
If this condition is met, then the two states can be connected by an isothermal as well as an adiabatic process.
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