91Ó°ÊÓ

1. The net work done by the cycle, ${\mathrm{W}}_{\mathrm{net}}=1.2\mathrm{J}$
2. The change in the internal energy along path ab,$∆{\mathrm{E}}_{\mathrm{int},\mathrm{ab}}=3.0\mathrm{J}$
3. The work done along path ab,${\mathrm{W}}_{\mathrm{ab}}=5\mathrm{J}$
4. The energy transferred to heat during path ca,${\mathrm{Q}}_{\mathrm{CA}}=2.5\mathrm{J}$

In this whole thermodynamic cycle, the use of first law of thermodynamics gives the heat produced, internal energy and the work done along a particular path by the body. The work done during a process of constant volume is zero. We use the first law of thermodynamics to calculate the heat along different paths.

Formulae:

The equation of first law of thermodynamics,${\mathrm{Q}}_{\mathrm{ab}}={\mathrm{W}}_{\mathrm{ab}}+∆{\mathrm{E}}_{\mathrm{int},\mathrm{ab}}$ …(¾±)

The total work done by the system, ${\mathrm{W}}_{\mathrm{net}}={\mathrm{Q}}_{\mathrm{ab}}+{\mathrm{Q}}_{\mathrm{bc}}+{\mathrm{Q}}_{\mathrm{ca}}$ …(¾±¾±)

We know that the process a to b is an expansion. So, work done W>0 for this path is $\mathrm{W}=5.0\mathrm{J}$.

We know that the change in internal energy during this path is $3.0\mathrm{J}$.

Applying the first law of thermodynamics to pathwe get the energy transferred as heat during process ab using equation (i) is given as:

$\begin{array}{rcl}{\mathrm{Q}}_{\mathrm{ab}}& =& 5.0\mathrm{J}+3.0\mathrm{J}\\ & =& 8.0\mathrm{J}\end{array}$

Hence, the energy transferred along ab is$8.0\mathrm{J}$

The net work done,${\mathrm{W}}_{\mathrm{net}}=1.2\mathrm{J}$

It is the same as the net heat (${\mathrm{Q}}_{\mathrm{ab}}+{\mathrm{Q}}_{\mathrm{bc}}+{\mathrm{Q}}_{\mathrm{ca}}$)

Also,${\mathrm{Q}}_{\mathrm{ca}}=2.5\mathrm{J}$

Thus, using equation (ii), we get the energy transferred as heat during bc as:

$\begin{array}{rcl}{\mathrm{Q}}_{\mathrm{bc}}& =& {\mathrm{W}}_{\mathrm{net}}-{\mathrm{Q}}_{\mathrm{ab}}+{\mathrm{Q}}_{\mathrm{ca}}\\ & =& \left(1.2-8.0-2.5\right)\mathrm{J}\\ & =& -9.3\mathrm{J}\end{array}$

Hence, the energy transferred during the process bc is -9.3 J.