Question

Derive the dimensions of specific heat that is defined as the amount of heat required to elevate the temperature of an object of mass 1 kg by 1 degree Celcius.

Answer 1

Dimension of specific heat will be
`=L^2T^(-2)\Theta ^(-1)`

Step-by-step explanation:

We know that heat
`Q=mc\Delta T`, Q is heat generated, m is mass, c is specific heat and
`\Delta T` is temperature difference

From formula we can write
`c=(Q)/(m* \Delta T)`

Now unit of Q is joule or N-m

Newton can be written as
`kgm/sec^2`

So unit of Q is
`kgm^2/sec^2`

For dimension we use M for kg, L for meter(m) ,T for sec and
`\Theta` for temperature

So dimension of Q is
`ML^2T^(-2)`

So dimension of specific heat will be
`(ML^2T^(-2))/(M\Theta )=L^2T^(-2)\Theta ^(-1)`