Two solid bodies of equal mass m initially at `T = 0^(@)C` are heated at a uniform and same rate under identical conditions. The temperature of the first object with latent heat `L_(1)` and specific heat capacity in solid state `C_(1)` changes according to graph `1` on the diagram. the temperature of the second object withe latent heat `L_(2)` and specific heat capacity in solid state `C_(2)` changes according to graph `2` on the diagram. based on what is shown on the graph, the latent heat `L_(1) and L_(2)` and the specific heat capacities `C_(1) and C_(2)` in solid state obey which of the following relationships?

Options

A. `L_(1) gt L_(2), C_(1) lt C_(2)`
B. `L_(1) lt L_(2), C_(1) lt C_(2)`
C. `L_(1) gt L_(2), C_(1) gt C_(2)`
D. `L_(1) lt L_(2), C_(1) gt C_(2)`

Answer

A

Explanation

If heat is supplied at constant rate `P`, then `Q = P Delta tau` and as during change of state `Q = mL, so,mL = P Delta t`
i.e., `L = [P/m] Delta t = P/m` (length of line `AB`)
Hence `L_(1) gt L_(2)`
i.e., the ratio of latent heat of fusion of the two substances are in the ratio `3:4`
In the portion `OA` the substance is in solid state and its temperature is changing.
`Delta Q = mCDelta T` and ` Delta Q = P Delta t`
so, `(Deltat)/(Delta t) = (P)/(mC)` or slope = `(P)/(mS) = [ "as" (Delta T)/(Delta t)="slope" ]`
Hence, `C_(1) lt C_(2)`.