JEE Advanced2013PhysicsThermal Properties of MatterActual
The figure below shows the variation of specific heat capacity ( C ) of a solid as a function of temperature ( T ). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement (s) is (are) correct to a reasonable approximation.
Options
- AThe rate at which heat is absorbed in the range 0 - 100   K varies linearly with temperature T.
- BHeat absorbed in increasing the temperature from 0 - 100   K is less than the heat required for increasin
- CThere is no change in the rate of heat absorption in the range 400 - 500   K .
- DThe rate of heat absorption increases in the range 200 - 300   K .
Correct answer
A. The rate at which heat is absorbed in the range 0 - 100   K varies linearly with temperature T.
Step-by-step solution
q  =  mCT dq dt = mc dT dt R = rate of absorption of heat = dq dt ∝ C (i) in 0 - 100   K The graph between ( 0 - 100   K ) appears to be a straight line upto a reasonable approximation. (ii) Δ q = mC Δ T as C is more in ( 400 - 500   K ) then ( 0 - 100   K ) so heat is increasing. (iii) C remains constant so there no change in R from ( 400 - 500   K ) (iv) C is increases so R is increases in range ( 200 - 300   K )