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Question
Solve the following problems:
Equal heat is given to two objects A and B of mass 1 g. Temperature of A increases by 3°C and B by 5°C. Which object has more specific heat? And by what factor?
Solution
\[s = \frac{∆ Q}{m ∆ T}\]
Let Q cal of heat is given to both A and B.
For body A,
\[s_1 = \frac{Q}{1 \times 3} = \frac{Q}{3} \text {cal }g^{- 1} {}^o C^{- 1}\]
For body B,
\[s_2 = \frac{Q}{1 \times 5} = \frac{Q}{5} \text { cal } g^{- 1} {}^o C^{- 1}\]
Now,
\[\frac{s_1}{s_2} = \frac{\frac{Q}{3}}{\frac{Q}{5}} = \frac{5}{3}\]
\[ \Rightarrow s_1 = \frac{5}{3} s_2\]
Thus, specific heat capacity of body A is more than body B and by a factor of \[\frac{5}{3}\].
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