- Home
- Standard 11
- Physics
10-1.Thermometry, Thermal Expansion and Calorimetry
medium
The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$, where $k$ is a constant of suitable dimensions in $SI$ units, and $T$ is the absolute temperature. If the heat required to raise the temperature of $1 \ kg$ of the substance from $-73^{\circ} C$ to $27^{\circ} C$ is $n k$, the value of $n$ is. . . . . .[Given: $0 K =-273^{\circ} C$.]
A
$20000$
B
$30000$
C
$40000$
D
$25000$
(IIT-2024)
Solution
$T _{ i }=-73^{\circ} C =200 K$
$T _{ f }=27^{\circ} C =300 K$
$Q =\int msdT$
$=\int 1 \cdot kT dT$
$=\int kT dT = K \int_{200}^{300} TdT$
$=\frac{ K }{2}\left[ T ^2\right]_{200}^{300}=\frac{ K }{2}\left[300^2-200^2\right]$
$Q =25000 K$
Hence $\eta=25000$
Standard 11
Physics
