Ncert Exercises & Solutions

What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, p_ext in a single step as shown in figure? Explain graphically.

Suppose total volume of the gases is V_i and pressure of the gas inside cylinder is p. After compression by constant external presure, (p_ext) in a single tap, final volume of the gas becomes V_f.

Then volume change,

∆ v = (V_{f} - V_{i})

If W is the work done on the system by movement of the piston, then

W = p_{ext} (- ∆ V)

W = - p_{ext} (V_{f} - V_{i})

This can be calculated from p-V graph as shown in the figure. Work done is equal to the shaded area

{ABV}_{f} V_{i}

The negative sign in this expression is required to obtain conventional sign for W which will be positive. Because in case of compression work is done on the system, so

∆ V

will be negative.

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