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

Question

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 (A) 800J (B) 373J (C) 273J (D) 400J

Tardigrade Admin · Accepted Answer

dQ=nCdT , dQ=nk(T3/θ 3) dT Q =( nk /θ3) ∫ T 1 T 2 T 3 dt =( nk /θ3)(( T 24- T 14/4)) =(2 × 1940(504-104)/(281)3 × 4)=272.79 J Q=273 J

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

$800 J$

$373 J$

$273 J$

$400 J$

$d Q = n C d T$ ,
$d Q = nk \frac{T ^{3}}{θ ^{3}} d T$
$Q = \frac{nk}{θ ^{3}} \int_{T_{1}}^{T_{2}} T^{3} d t = \frac{nk}{θ ^{3}} (\frac{T _{2}^{4} - T _{1}^{4}}{4})$
$= \frac{2 \times 1940 ( 5 0 ^{4} - 1 0 ^{4} )}{( 281 ) ^{3} \times 4} = 272.79 J$
$Q = 273 J$

Q. The molar heat capacity of rock salt at low temperatures varies with temperature according to Debye's law; C=kθ3T3​ where k=1940Jmol−1K−1 and θ=281K . The heat required to raise the temperature of 2 moles of rock salt from 10K to 50K is

800J

373J

273J

400J