The specific heat of a metal at low temperatures varies according to S=(4 / 5) 73, where T is the absolute temperature. Find the heat energy (in SI unit) needed to raise the temperature of unit mass of the metal from T=1 K to T=2 K.

Question

The specific heat of a metal at low temperatures varies according to S=(4 / 5) 73, where T is the absolute temperature. Find the heat energy (in SI unit) needed to raise the temperature of unit mass of the metal from T=1 K to T=2 K. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Q=∫ m S d T=(m T4/5) ⇒ (Q/m)=(15/5)=3 unit

Q. The specific heat of a metal at low temperatures varies according to $S = (4/5) 7^{3}$ , where $T$ is the absolute temperature. Find the heat energy (in $S I$ unit) needed to raise the temperature of unit mass of the metal from $T = 1 K$ to $T = 2 K$ .

$Q = \int m S d T = \frac{m T ^{4}}{5}$
$\Rightarrow \frac{Q}{m} = \frac{15}{5} = 3$ unit

Q. The specific heat of a metal at low temperatures varies according to S=(4/5)73, where T is the absolute temperature. Find the heat energy (in SI unit) needed to raise the temperature of unit mass of the metal from T=1K to T=2K.

Q=∫mSdT=5mT4​ ⇒mQ​=515​=3 unit

Q. The specific heat of a metal at low temperatures varies according to $S = (4/5) 7^{3}$ , where $T$ is the absolute temperature. Find the heat energy (in $S I$ unit) needed to raise the temperature of unit mass of the metal from $T = 1 K$ to $T = 2 K$ .

$Q = \int m S d T = \frac{m T ^{4}}{5}$
$\Rightarrow \frac{Q}{m} = \frac{15}{5} = 3$ unit