A) \[{{L}_{1}}>{{L}_{2}};\text{ }{{C}_{1}}<{{C}_{2}}\]
B) \[{{L}_{1}}<{{L}_{2}};\text{ }{{C}_{1}}<{{C}_{2}}\]
C) \[{{L}_{1}}>{{L}_{2}};\text{ }{{C}_{1}}>{{C}_{2}}\]
D) \[{{L}_{1}}<{{L}_{2}};\text{ }{{C}_{1}}>{{C}_{2}}\]
Correct Answer: A
Solution :
If heat is supplied at constant rate P, then \[Q=P\Delta t\]and as during change of state \[Q=mL\], so, \[mL=P\Delta t\] |
i.e., \[L=\left[ \frac{P}{m} \right]\Delta t=\frac{P}{m}\] (length of line AB) |
Hence, \[{{L}_{1}}>{{L}_{2}}\] |
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. |
\[\Delta Q=mC\Delta T\] and \[\Delta Q=P\Delta t\] |
So, \[\frac{\Delta T}{\Delta t}=\frac{P}{mC}\] or \[slope=\frac{P}{mS}\] |
\[=\left[ as\frac{\Delta T}{\Delta t}=slope \right]\,\,;\] Hence \[{{C}_{1}}<{{C}_{2}}\] |
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