We have measured the thermal conductivities and electrical resistivities of Y
1Ba
2Cu
3O
7-y, Er
1Ba
2Cu
3O
7-y and Bi
1Sr
1Ca
1Cu
2O
y compounds using the steady-state comparative method and conventional four-probe method. Below the transition temperature, T
c, the thermal conductivities had strikingly large values and a maximum value. By applying the Wiedemann-Franz law, λR/T=L
0, with the electrical resistivity data at T
c, the phonon-thermal conductivities were found to predominate in those superconductors. The normalizations of the measured thermal conductivities of those superconductors with respect to λ
C, critical thermal conductivity, show that the temperature dependence of the thermal conductivity of Y
1Ba
2Cu
3O
7-y is similar to the dependence of La
1.8Sr
0.2Cu
1O
4-y, Er
1Ba
2Cu
3O
7-y and Bi
1Sr
1Ca
1Cu
2O
y compounds. Most of the normalized thermal conductivities agree with our theory, λ
s=2ξ
2·λ
n/(1+ξ
4), in which the value n of the phonon thermal conductivity in the form λ
n=ξ
n in the normal conducting state is between -1 and -1.5 below T
c.
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