A certain substance has a mass of 50 g / mole. When 300 J of heat… - Vidyadip

Question

A certain substance has a mass of $50 g /$ mole. When 300 J of heat is added to 25 g of sample of this material, its temperature rises from $25^{\circ} C$ to $45^{\circ} C$. Calculate
i. the thermal capacity,
ii. specific heat capacity, and
iii. molar heat capacity of the sample.

✓

Answer

i. Total heat supplied to sample $\Delta Q =300 J$ and rise in temperature $\Delta T = T _2- T _1=45-25=20^{\circ} C$
$\therefore$ Thermal capacity of substance is given as $=\frac{\Delta Q}{\Delta T}=\frac{300}{20}=15 J^0 C ^{-1}$
ii. mass, $m =25 g=0.025 kg$
$\therefore$ Specific heat capacity, $c =\frac{1}{m} \cdot \frac{\Delta Q}{\Delta T}=\frac{1}{0.025} \times 15=600 Jkg ^{-1}{ }^{ o } C ^{-1}$
iii. Number of moles in 25 g sample of $50 g / mol$ is
$\mu=\frac{25}{50}=0.5$ moles
$\therefore$ Molar heat capacity $C =\frac{1}{\mu} \frac{\Delta Q}{\Delta T}=\frac{1}{0.5} \times 15=30 Jmol ^{-10} C ^{-1}$.

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