3. (Pts 15) For the idealized reversible Carnot cycle shown here in the T-S diagram (see figure), please analytically prove the relation below used to establish the Thermodynamic Temperature Scale

as discussed in class: (Please show your detailed steps/derivations) \frac{\mathrm{Q}_{\mathrm{H}}}{\mathrm{Q}_{\mathrm{L}}}=\frac{\mathrm{T}_{\mathrm{H}}}{\mathrm{T}_{\mathrm{L}}}