  The thermodynamic behavior of the spin $S=1/2$ antiferromagnetic two-leg
ladder compound $(C_{5}H_{12}N)_{2} CuBr_{4}$ in a uniform magnetic field is
studied using numerical and analytical approaches. The entropy $S(H,T)$ and
specific heat $C(H,T)$ are calculated. The specific heat shows various
behaviors in different regions of the magnetic field. The field-dependence of
the specific heat is almost symmetric about the average of quantum critical
fields in complete agreement with experimental results. In addition, it is
found that during an adiabatic demagnetization process, temperature drops in
the vicinity of the field induced zero-temperature quantum phase transitions.
