A) \[{{t}_{1}}={{t}_{2}}={{t}_{3}}\]
B) \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]
C) \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]
D) \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]
Correct Answer: B
Solution :
The rate of cooling is given as \[\frac{dQ}{dt}=K({{T}_{1}}-{{T}_{2}})\] ...(i) where\[({{T}_{1}}-{{T}_{2}})\]is temperature difference between the temperature of body and surroundings. Since, the temperature difference between \[75{}^\circ C\]and surrounding temperature is greater than the temperature difference between \[70{}^\circ C\]and surrounding temperature Hence, \[{{t}_{1}}<{{t}_{2}}\] ...(2) Similarly, the temperature difference between \[70{}^\circ C\]and surrounding temperature is greater than temperature difference between\[65{}^\circ C\] and surrounding temperature. Hence, \[{{t}_{2}}<{{t}_{3}}\] ...(3) Thus, from eqs. (2) and (3), \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]
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