As illustrated in the figure, a substance undergoes the process abc...

From the given P-V diagram, the process $abc$ consists of an isobaric process $ab$ and an isochoric process $bc$.

The work done during the isobaric process $ab$ is:
$W_{ab} = P(V_b - V_a) = 200 \times 10^3 \times (0.05 - 0.02) = 6000 \text{ J}$

The work done during the isochoric process $bc$ is zero since the volume is constant:
$W_{bc} = 0$

Total work done by the system is:
$W = W_{ab} + W_{bc} = 6000 \text{ J}$

According to the first law of thermodynamics, the total heat supplied in Joules is:
$Q = \Delta U + W = 5000 \text{ J} + 6000 \text{ J} = 11000 \text{ J}$

Given that the heat supplied is $2625 \text{ cal}$, the mechanical equivalent of heat $J$ is:
$J = \dfrac{11000 \text{ J}}{2625 \text{ cal}} \approx 4.19 \text{ J/cal}$