Consider the idealized dual$-$loop cycle shown below:

Compute the ratio of mass flow rates power to refrigeration cycle, $\frac{m_P^{}}{m_R^{}}$ such that the power

turbine will produce just enough power to drive the refrigeration compressor. Assume R$-12$ is

the working fluid with the following known

State $1$: $110C,$ saturated vapor

State $3$: $50C,$ saturated liquid

State $8$:$-15C,$ saturated vapor