The specific heat capacity of a substance is temperature dependent and is given by the formula where is a constant of suitable dimensions in SI units, and is the absolute temperature. If the heat required to raise the temperature of of the substance f

Question

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 $- 73 ° C$ to $27 ° C$ is $n k$ , the value of $n$ is _____. $[Given: 0 K = - 273 ° C .]$ [2024]

Smart Achievers · Accepted Answer

(25000)

$Given, mass m = 1 kg,$

$T_{i} = - 73 ° C = 200 K$

$T_{f} = 27 ° C = 300 K$

$Q = m c d T = 1 \cdot k T d T$

$Q = \int_{200}^{300} 1 \cdot k T d T = k \int_{200}^{300} T d T$

$= \frac{k}{2} {[T^{2}]}_{200}^{300} = \frac{k}{2} [300^{2} - 200^{2}] = 25000 K$

$Hence n = 25000$

Solution

Ans.
(25000)

$Given, mass m = 1 kg,$

$T_{i} = - 73 ° C = 200 K$

$T_{f} = 27 ° C = 300 K$

$Q = m c d T = 1 \cdot k T d T$

$Q = \int_{200}^{300} 1 \cdot k T d T = k \int_{200}^{300} T d T$

$= \frac{k}{2} {[T^{2}]}_{200}^{300} = \frac{k}{2} [300^{2} - 200^{2}] = 25000 K$

$Hence n = 25000$

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Solution

Ans. (25000) Given, mass m=1 kg, Ti=-73°C=200 K Tf=27°C=300 K Q=mc dT=1·kT dT Q=∫2003001·kT dT=k∫200300T dT =k2[T2]200300=k2[3002-2002]=25000 K Hence n=25000

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Ans.
(25000)

$Given, mass m = 1 kg,$

$T_{i} = - 73 ° C = 200 K$

$T_{f} = 27 ° C = 300 K$

$Q = m c d T = 1 \cdot k T d T$

$Q = \int_{200}^{300} 1 \cdot k T d T = k \int_{200}^{300} T d T$

$= \frac{k}{2} {[T^{2}]}_{200}^{300} = \frac{k}{2} [300^{2} - 200^{2}] = 25000 K$

$Hence n = 25000$