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10-1.Thermometry, Thermal Expansion and Calorimetry
hard
A system $S$ receives heat continuously from an electrical heater of power $10W$. The temperature of S becomes constant at $50^o C$ when the surrounding temperature is $20^o C$. After the heater is switched off, $S$ cools from $35.1^o C$ to $34.9^o C$ in $1$ minute. The heat capacity of $S$ is........ $ J/^oC$
A
$100$
B
$300$
C
$750$
D
$1500$
Solution
At $50^{\circ} \mathrm{C}, \frac{d Q}{d t}=k(50-20)=10$
$\therefore k=\frac{1}{3}$
at an average temperature of $35^{\circ} \mathrm{C}$
$\frac{d Q}{d t}=\frac{1}{3}(35-20)=5 J / s$
Heat lost in $1\, minute$ $=\frac{d Q}{d t} \times 60=300 \mathrm{J}$
Fall in temperature $=0.2^{\circ} \mathrm{C}=\Delta \theta$
$\therefore C=\frac{Q}{\Delta \theta}=\frac{300}{0.2^{\circ} \mathrm{C}}=1500 \mathrm{J} /^{\circ} \mathrm{C}$
Standard 11
Physics
