Understanding Heat Capacity and Work: Clarifying Misconceptions

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Ahmed1029
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In defining the heat capacity of a subatance as the constant relating change in temperature to change in heat, is it assumed that the system does no work? Does it really say (heat capacity is the constant relating heat change to temperature change when the system does no work)?
 
There is a ##c_v## and a ##c_p##. The latter is larger -- that is an indication the system does work.

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