According to Debye's T3 law, the specific heat of many solids at low temperature T vanes acceding to the relation C=2T3, where a is constant. The heat energy required to raise the temperature of 4kg mass from T=1 to T=3K

Question

According to Debye's T3 law, the specific heat of many solids at low temperature T vanes acceding to the relation C=2T3, where a is constant. The heat energy required to raise the temperature of 4kg mass from T=1 to T=3K  (A)  208 text α  (B)  20 text α  (C)  80 text α  (D)  text8 α

Tardigrade Admin · Accepted Answer

Since, dQ=mc dT ⇒ Q∫dQ=mα ∫13T3dT ⇒ Q=4α [ (T4/4) ]13 ⇒ Q=α [(3)4-(1)4]=α (81-1) ⇒ Q=80 α

Q. According to Debye's $T^{3}$ law, the specific heat of many solids at low temperature T vanes acceding to the relation $C = 2 T^{3},$ where a is constant. The heat energy required to raise the temperature of 4kg mass from $T = 1$ to $T = 3 K$

$208 α$

$20 α$

$80 α$

$8 α$

Since, $d Q = m c d T$
$\Rightarrow$ $Q \int d Q = m α \int_{1}^{3} T^{3} d T$
$\Rightarrow$ $Q = 4 α [\frac{T ^{4}}{4}]_{1}^{3}$
$\Rightarrow$ $Q = α [(3)^{4} - (1)^{4}] = α (81 - 1)$
$\Rightarrow$ $Q = 80 α$

Q. According to Debye's T3 law, the specific heat of many solids at low temperature T vanes acceding to the relation C=2T3, where a is constant. The heat energy required to raise the temperature of 4kg mass from T=1 to T=3K

208α

20α

80α

8 α