The figure below shows the variation of specific heat capacity ( C ) of a solid as a function of temperature…

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.
  1. The rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T.
  2. Heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from400-500K.
  3. There is no change in the rate of heat absorption in the range 400-500 K.
  4. The rate of heat absorption increases in the range 200-300 K.

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)

Asked in: JEE Advanced 2013 (Paper 2)

Practice more Thermal Properties of Matter questions on Aicharya