Question

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

Answer 1

Answer:

ΔT ∝ $\frac{1}{m}$

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:

$\Delta T=\frac{Q_{in}}{mc}$

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:

$\Delta T=\frac{Q_{in}}{c}\times \frac{1}{m}\\\\\Delta T=\frac{K}{m}$

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

⇒ ΔT ∝ $\frac{1}{m}$

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