  We investigate the formation of dust grains in the ejecta of a SN IIb and
their evolution in the shocked gas in the SNR by considering the uniform and
power-law density structures for the CSM. Based on these calculations, we also
simulate the time evolution of thermal emission from the shock-heated dust in
the SNR and compare the results with the observations of Cas A SNR. We find
that the total mass of dust formed in the SN IIb is as large as 0.167 M_sun but
the average radius of dust is smaller than 0.01 mum and is significantly
different from those in SNe II-P with the massive H-envelope. In the explosion
with the small-mass H-envelope, the expanding He core undergoes little
deceleration, so that the gas density in the He core is too low for large-sized
grains to form. In addition, the low-mass H-envelope of the SN IIb leads to the
early arrival of the reverse shock at the dust-forming region. If the CSM is
more or less spherical, therefore, the newly formed grains would be completely
destroyed in the relatively dense shocked gas for the CSM density of n_H > 0.1
cm^{-3}. However, the actual CSM is likely to be non-spherical, so that a part
of grains could be ejected into the ISM without being shocked. We demonstrate
that the time evolution of the SED by thermal dust emission is sensitive to the
ambient gas density and structure that affects the passage of the reverse shock
into the ejecta. Thus, the SED evolution well reflects the evolution of dust
through erosion by sputtering and stochastic heating. For Cas A, we consider
the CSM produced by the steady mass loss of ~8x10^{-5} M_sun/yr during the
supergiant phase. Then we find the infrared SED of Cas A is reasonably
reproduced by thermal emission from the newly formed dust of 0.08 M_sun, which
consists of 0.008 M_sun shocked warm dust and 0.072 M_sun unshocked cold dust.
