Question

Explain why the temperature rise of a body is INVERSELY PROPORTIONAL to its mass for the same heat energy input ?

Answer 1

ΔT ∝
`(1)/(m)`

Step-by-step explanation:

We know that, the heat input to a body is given as:

`Q_(in)=mc\Delta T`

Where,

`Q_(in) \to \textrm{Heat in}\\m\to \textrm{mass of the body}\\c\to \textrm{Specific heat capacity of the body}\\\Delta T\to\textrm{Temperature rise of the body}`

Specific heat capacity of a body depends on its material and thus is constant for a given body.

Rewriting the above equation in terms of
`\Delta T`, we get:

`\Delta T=(Q_(in))/(mc)`

Now, as per given question, the heat supply to the given body is a constant.

Therefore, replacing the constant quantities by a constant 'K', we get:

`\Delta T=(Q_(in))/(c)* (1)/(m)\\\\\Delta T=(K)/(m)`

So, rise in temperature is a function of the mass only and varies inversely with the mass.

⇒ ΔT ∝
`(1)/(m)`

Therefore, the temperature rise of a body is INVERSELY PROPORTIONAL to its mass for the same heat energy input.