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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

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

Grade:11

2 Answers

Swapnil Saxena
102 Points
10 years ago

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.)

Rishi Sharma
askIITians Faculty 646 Points
one year ago
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

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