The specific heat of a metal at low temperature varies according to S=aT^3 where a is a constant and T is absolute temperature. The heat energy needed to raise unit mass of the metal from temperature T=1K to T=2K is

a) 3a

b) 15a/4

c) 2a/3

d) 13a/4

We know that the dQ = mS(dT)

then Q= ∫mSdT

Since S=aT³ where a is a constant . substituting the value of S

Q= ∫m(aT³)dt= maT⁴/4

if the integration is done form 1 K to 2 K of unit mass then the result is (a(2)⁴/4)-(a(1)⁴/4)= 15a/4 (b.)

Dear Student,
Please find below the solution to your problem.

We know that the dQ = mS(dT)
then Q= ∫mSdT
Since S=aT3 where a is a constant . substituting the value of S
Q= ∫m(aT3)dt= maT4/4
if the integration is done form 1 K to 2 K of unit mass then the result is (a(2)4/4)-(a(1)4/4)= 15a/4

Thanks and Regards