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Home » Consider that an ideal gas is expanding in a process given by P = f(V), which passes through a point (V0, P0). Show that the gas is absorbing heat at (P0, V0) if the slope of the curve P = f(V) is larger than the slope of the adiabat passing through (P0, V0).
Consider that an ideal gas is expanding in a process given by P = f(V), which passes through a point (V0, P0). Show that the gas is absorbing heat at (P0, V0) if the slope of the curve P = f(V) is larger than the slope of the adiabat passing through (P0, V0).
CBSE | Class 11 | NCERT Exemplar | Physics | Thermodynamics
Consider that an ideal gas is expanding in a process given by P = f(V), which passes through a point (V0, P0). Show that the gas is absorbing heat at (P0, V0) if the slope of the curve P = f(V) is larger than the slope of the adiabat passing through (P0, V0).

 Answer:

The slope of the graph as given by:

\left( {{V}_{0}},{{P}_{0}} \right)={{\left( \frac{dP}{dV} \right)}_{{{V}_{0}},{{P}_{0}}}}

Making use of the above relation, we can determine that

{{V}_{0}}{{f}^{'}}({{V}_{0}})>-\gamma {{P}_{0}}

{{f}^{'}}({{V}_{0}})>\frac{-\gamma {{P}_{0}}}{{{V}_{0}}}

i

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