Question
Thermal capacity of $$40\,g$$ of aluminium $$\left( {s = 0.2\,cal/g - K} \right)$$ is
A.
$$168\,J{/^ \circ }C$$
B.
$$672\,J{/^ \circ }C$$
C.
$$840\,J{/^ \circ }C$$
D.
$$33.6\,J{/^ \circ }C$$
Answer :
$$33.6\,J{/^ \circ }C$$
Solution :
Thermal capacity of a body is defined as the amount of heat required to raise the temperature of the (whole) body through $${1^ \circ }C$$ or $$1K.$$
Amount of heat energy required $$\left( {\Delta Q} \right)$$ to raise the temperature of mass $$m$$ of a body through temperature range $$\left( {\Delta T} \right)$$ is $$\Delta Q = sm\left( {\Delta T} \right)$$
where, $$s$$ is specific heat of the body,
when $$\Delta T = 1K,\Delta Q =$$ thermal capacity
∴ Thermal capacity $$ = s \times m \times 1$$
$$ = ms$$
Here, $$m = 40\,g,s = 0.2\,cal/g\,K$$
∴ Thermal capacity $$ = 40 \times 0.2 = 8\,cal{/^ \circ }C$$
$$ = 4.2 \times 8\,J{/^ \circ }C = 33.6\,J{/^ \circ }C$$