Question

Which of the substances $A,B$ and $C$ has the lowest heat capacity if heat is supplied to all of them at equal rates. The temperatures versus time graph is shown.

• A. $A$
• B. $B$
• C. $C$
• D. All have equal specific heat

Answer 1

Answer: (A)

$A$

Given: Temperature vs time graph

Heat Rates (Q¹) are equal

Solution:

Heat energy supplied, Q=cT ( T is temperature, c is heat capacity)

Heat rate, Q¹=$\frac{Q}{t}$

$\Rightarrow$Q=Q¹t

Therefore,Q¹t =cT

$\Rightarrow$ T=$\frac{Q^1}{c}\times t$

Comparing with y=mx, we get

Slope,m= $\frac{Q^1}{c}$

Thus, for lowest heat capacity , slope m should be greatest.

Since, Slope m is greatest, A has lowest heat capacity.

Hence, Option A is correct.