Question

the specific heat of a metal at low temperature varies according to S=aT^3 where a is constant and T is Absolute Temperature the heat energy needed to rise unit mass of the metal from T=1K to T=2K is ​

Answer 1

the specific heat of a metal at low temperature varies according to S=aT^3 where a is constant and T is Absolute Temperature the heat energy needed to rise unit mass of the metal from T=1K to T=2K is ​=

At temperature t the heat energy required to raise temperature of unit mass by dt is dq = at³ * 1*dt

So heat required to raise temperature from 1K to 2K is

∫$\int\limits^0_q \, dq$ = $\int\limits^1_2 {at3} \, dt$

=> q = a (16-1)/4

=> q = 15a/4