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Heat capacity (CP) is an extensive property but specific heat (c) is an intensive property. What will be the relation between Cp and c for 1 mol of water?

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The relation between heat capacity (CpCp) and specific heat (cc) for 1 mole of a substance, such as water, can be derived from their definitions. Heat Capacity (CpCp): Heat capacity (CpCp) is an extensive property, meaning it depends on the amount of substance present. It is defined as the amount...
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The relation between heat capacity (CpCp) and specific heat (cc) for 1 mole of a substance, such as water, can be derived from their definitions.

  1. Heat Capacity (CpCp): Heat capacity (CpCp) is an extensive property, meaning it depends on the amount of substance present. It is defined as the amount of heat required to raise the temperature of a given amount of substance by 1 degree Celsius (or 1 Kelvin).

Cp=n×cCp=n×c

Where:

  • nn is the number of moles of the substance.
  • cc is the specific heat capacity of the substance.
  1. Specific Heat (cc): Specific heat (cc) is an intensive property, meaning it does not depend on the amount of substance present. It is defined as the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius (or 1 Kelvin).

c=Cpnc=nCp

For 1 mole of water (n=1 moln=1mol), the relation between CpCp and cc becomes:

c=Cp1=Cpc=1Cp=Cp

Therefore, for 1 mole of water, the specific heat (cc) is equal to the heat capacity (CpCp). In other words, the specific heat of 1 mole of water is numerically equal to its heat capacity.

 
 
 
 
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