Question

Arrange the following substances in the increasing order of their heat capacity.

Substance	Mass	Initial Temperature	Final temperature	Heat Absorbed
a	$10g$	$5^{o}C$	$5^{o}C$	$100cal$
b	$20g$	${20}^{o}C$	$5^{o}C$	$200cal$
c	$30g$	${40}^{o}C$	${40}^{o}C$	$400cal$

• A. ABC
• B. BAC
• C. CAB
• D. ACB

Answer 1

The correct option is B

BAC

Step 1: Recall the formula for heat capacity-

We know that $Q=s∆T$, where $s$ is heat capacity. So, $s=\frac{Q}{∆T}$. We are given $Q,m,∆T$ for substances a,b, and c.

Note that we are not including the mass of the substance, as we are asked about heat capacity and not specific heat. First, we will compute them and then arrange them in increasing order.

Step 2: Calculate Heat capacity for substance $A$-

For substance A, $s=\frac{Q}{∆T}=\frac{100}{(10-5)}=20cal{}^o{C}^{-1}$
For substance B,$s=\frac{Q}{∆T}=\frac{200}{(50-20)}=\frac{20}{3}cal{}^o{C}^{-1}$

For substance C, $s=\frac{Q}{∆T}=\frac{400}{(50-40)}=40cal{}^o{C}^{-1}$

Step 3: Arrange in increasing order-

We can see that B has the least heat capacity, then A has $\frac{20}{3}cal{}^o{C}^{-1}$ the capacity and then C has the highest heat capacity.

So, the correct option is (B) BAC.