A) \[{{\text{r}}_{\text{1}}}={{\text{t}}_{\text{2}}}={{\text{t}}_{\text{3}}}\]
B) \[{{\text{r}}_{\text{1}}}\text{}{{\text{t}}_{\text{2}}}\text{}{{\text{t}}_{\text{3}}}\]
C) \[{{\text{r}}_{\text{1}}}\text{}{{\text{t}}_{\text{2}}}\text{}{{\text{t}}_{\text{3}}}\]
D) \[{{\text{r}}_{\text{1}}}\text{}{{\text{t}}_{\text{2}}}\text{}{{\text{t}}_{\text{3}}}\]
Correct Answer: B
Solution :
From Newtons law of cooling, rate of cooling is given by \[\frac{dQ}{dt}=K\,({{T}_{1}}-{{T}_{2}})\]. ... (i) where \[({{T}_{1}}-{{T}_{2}})\] is temperature difference. Since, temperature difference between \[{{75}^{o}}C\] and surrounding temperature is greater than the temperature difference between \[{{70}^{o}}C\]and surrounding temperature, hence \[{{t}_{1}}<{{t}_{2}}\] ... (i) Similarly, the temperature difference between \[{{70}^{o}}C\] and surrounding temperature is greater than temperature difference between \[{{65}^{o}}C\] and surrounding temperature. Hence, \[{{t}_{2}}<{{t}_{3}}\] ..? (ii) Hence, \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]
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