1. Tardigrade
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  3. Physics
  4. The molar heat capacity of rock salt at low temperatures varies with temperature according to Debye's law; C=k(T3/θ 3) where k=1940 J mol- 1 K- 1 and θ =281 K . The heat required to raise the temperature of 2 moles of rock salt from 10 K to 50 K is

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Q. The molar heat capacity of rock salt at low temperatures varies with temperature according to Debye's law; $C=k\frac{T^{3}}{\theta ^{3}}$ where $k=1940 \, J \, mol^{- 1} \, K^{- 1}$ and $\theta =281 \, K$ . The heat required to raise the temperature of $2$ moles of rock salt from $10 \, K$ to $50 \, K$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$dQ=nCdT$ ,
$dQ=nk\frac{T^{3}}{\theta ^{3}} \, dT$
$Q =\frac{ nk }{\theta^{3}} \int_{ T _{1}}^{ T _{2}} T ^{3} dt =\frac{ nk }{\theta^{3}}\left(\frac{ T _{2}^{4}- T _{1}^{4}}{4}\right)$
$=\frac{2 \times 1940\left(50^{4}-10^{4}\right)}{(281)^{3} \times 4}=272.79 J$
$Q=273 \, J$