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**Hint:**Such a system must obey the first law of thermodynamics. Use the equation of the first law of thermodynamics to find the work done by the system.

Formula used: In this solution we will be using the following formulae;

\[\Delta U = \Delta Q - W\] where \[\Delta U\] is the change in internal energy of the system, \[\Delta Q\] is the change in thermal energy of (or the heat absorbed by) the system, and \[W\] is the work done by the system.

\[\Delta Q = m{c_p}\Delta T\] where \[m\]is the mass of the gas, \[{c_p}\]is the specific heat at constant pressure, and \[\Delta T\] is the change in temperature of the system.

\[\Delta U = m{c_v}\Delta T\] where \[{c_v}\] is the specific capacity at constant volume.

**Complete Step-by-Step Solution:**

When the gas is heated, the change in thermal energy would be given by

\[\Delta Q = m{c_p}\Delta T\]where \[m\] is the mass of the gas, \[{c_p}\] is the specific heat at constant pressure, and \[\Delta T\] is the change in temperature of the system.

At the same time, the change in internal energy is given by

\[\Delta U = m{c_v}\Delta T\] where \[{c_v}\] is the specific capacity at constant volume.

Now, from the first law of thermodynamics given as

\[\Delta U = \Delta Q - W\] where \[W\] is the work done by the system, we can find the work done as

\[W = \Delta Q - \Delta U\]

\[\dfrac{W}{{\Delta Q}} = \dfrac{{\Delta Q - \Delta U}}{{\Delta Q}} = 1 - \dfrac{{\Delta U}}{{\Delta Q}}\]

Replacing the known expressions into above equation, we have

\[\dfrac{W}{{\Delta Q}} = 1 - \dfrac{{m{c_v}\Delta T}}{{m{c_p}\Delta T}} = 1 - \dfrac{{{c_v}}}{{{c_p}}}\]

The ratio \[\dfrac{{{c_p}}}{{{c_v}}}\] is usually given the constant \[\gamma \]

Hence,

\[\dfrac{W}{{\Delta Q}} = 1 - \dfrac{1}{\gamma }\]

**Thus, the correct option is B**

**Note:**To avoid confusions, the thermodynamic equation can be written as

\[\Delta U = \Delta Q + W\]

However, in this format, the definition of \[W\] is the work done on (not by) the system. Hence, it is negative in value when work is done by the system

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