Question

One J/kg = _____ cal/g.

Answer 1

Hint: To solve this problem, first we need to find relation between 1 calorie and joules so during the conversion from j/kg to cl/g we don’t need to change units on every step, further we will discuss about the actual meaning of 1 calorie and 1 joule in terms of raise in temperature of water and work done on object.

Formula used:
1 joule=$\dfrac{1}{4.184}$calorie.

Complete Step by step solution:
The calorie is a unit of energy defined as the amount of heat needed to raise a quantity of water by one degree of temperature and joule is the derived unit of energy and is defined as the work done on or energy transferred to an object by applying a force of one newton to displace a body by one metre (to the direction of force).

Now, 1 kg = 1000g,
So,$1{J}/{kg=1{J}/{1000g}\;}\;$ and we know that 1 joule = $\dfrac{1}{4.184}$calorie so,

By putting this value in above equation we have,
$1{J}/{kg=1{J}/{1000g}\;}\;={\dfrac{1}{4.184}cal}/{1000g}\;=23.9\times {{10}^{-5}}{cal}/{g}\;$

Additional information:
In physics to solve many problems under different units The conversion of units plays a very crucial part, this can help to reduce complexity of problems by simple calculation between the same units in the SI system.

Note:
In above solution we have considered small calorie for our use which is defined as a heat required to rise a temperature of 1 gm of water by 1 degree Celsius and spelled with lower case “c”, and the other one is large calorie in which heat required to rise a temperature of 1 kg of water by one degree Celsius which is 1000x greater than small calorie and spelled as upper case ”C”.