Question

The specific heat of water is 1 cal ${g^{ - 1}}^ \circ {C^{ - 1}}$ . Its value in the S.I unit is approximately.
A. 1
B. 4.2
C. 420
D. 4200

Answer 1

Hint: These questions are based on conversions of units and also S.I units of terms like specific heat and to answer the questions you should know the basic knowledge of specific heat and its different values in different units such as value of specific heat in SI units and how to convert CGS to SI.

Complete Step-by-Step solution:
According to the question we are given specific heat of water in CGS which is 1 cal
We know that the value of 1 cal is = 4.2 joule (J).
In the question the value is given in gram so we know that 1 g= $\dfrac{1}{{1000}}$kg which is equal to 0.001 kg.
To change the CGS unit in SI we have to divide the values of 1 cal to that of 1 g which is = $\dfrac{{4.2J}}{{0.001k{g^ \circ }C}} = 4200J/k{g^ \circ }C$
Thus, the value of specific heat in SI is 4200 J/kg.
Hence, option D is correct.

Note: In SI units, specific heat is the amount of heat provided by joules to lift 1 gram of a substance. It can also manifest itself as J/Kg K. specific heat capacity may also be measured in calorie units per gram Celsius. We know that water has the highest specific heat strength of any liquid and for water the specific heat number is one calorie per vapor or 4.184 joules per joules.