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 form 0 to 500K at a constant rate. Ignoring any volume change, the following statement (s) is (are) correct to a reasonable approximation.

Options

A. The rate at which heat is absorbed in the range `0-100` K varies linearly with temperature T.
B. Heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400-500 K.
C. There is no change in the rate of heat absorption in the range 400-500 K.
D. The rate of heat absorption increases in the range 200-300 K .

Answer

b, c, d

Explanation

According to definition of specific heat capacity , `C = ( Delta Q)/(m Delta T)`
`rArr Delta Q = m C Delta T :. ( Delta Q)/(Delta t) = mC (Delta T)/(Delta t) `
Rate of heat absorbed ` = R = (Delta Q)/(Delta t) `
` rArr (Delta Q)/(Delta t) propto C`
(a) In ` 0 - 100 K`,
C increases with T but not linearly . So R increases but not linearly.
(b) As `Delta Q = m C Delta T`
`Q = m int C Delta T = ` area under C - T curve
From the graph it is clear that area under C - T is more in 400 - 500 K than in 0 - 100 K.
Therefore, heat absorbed in 0 - 100 K is less in 400 - 500 K.
(c ) In 400 - 500 K, C remains constant so there is no change in R.
(d) In 200 - 300 K, C increases so R increases.