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posted by HUYGEn .
Calculate the specific heat (\rm{J/g \; ^\circ C}) for a 21.5 g sample of a metal that absorbs 685 J when temperature increases from 42.1^\circ C to83.2^\circ C

You could save yourself a lot of typing woes if you omitted all of those extraneous symbols. I know you're trying to help us understand the problem because all of those symbols aren't available on keyboards but we've been a this long enough to know what the keyboards mean.
q = mass x specific heat x delta T.
q = 685 J. Substitute for the other variables and solve for specific heat.
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