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# Calculate heat required to raise the temperature of 1 g of water by 1$^{\circ}$ C ?

Last updated date: 13th Jun 2024
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Hint: We need to know the specific heat of water in order for us to determine the amount of heat required to raise the temperature of a given mass of water by 1 degree as can be seen in the formula.

Formula used:
Specific heat for a substance is given by:
$c = \dfrac{\Delta Q}{M \Delta T}$
where Q is used to denote heat, T is for temperature and M is for mass.

The specific heat of a substance is defined as the amount of heat required to raise the temperature of unit mass of the substance through one degree. As we are given 1 g of mass of water and the temperature has to be raised by 1$^{\circ}$ C, we will get the amount of heat to be numerically equal to specific heat:
$\implies c = \Delta Q$.
Now, in c.g.s. units, the specific heat of water is c = 1 cal $g^{-1 \circ} C^{-1}$. Therefore the heat required will be 1 calorie.
Therefore, the heat required to raise the temperature of 1 g of water by 1$^{\circ}$ C is 1 cal.
In MKS units, 1 calorie = 4.186 joule.

The MKS unit for specific heat is J $kg^{-1} K^{-1}$ whereas c.g.s. unit is cal $g^{-1 \circ} C^{-1}$. To make a conversion of specific heat from c.g.s. to MKS, one must first use the relation:
$1 cal g^{-1 \circ} C^{-1} = 4200 J kg^{-1 \circ} C^{-1}$.
T (in K) = t( in $^{\circ}$ C) + 273.