Question
Download Solution PDFA body cools from 70°C to 40°C in 5 minute. Calculate the time it takes to cool from 50°C to 20°C, the temperature of the surroundings is 10°C.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Using Newton's Laws of cooling,
Rate of cooling,
\(\frac{dT}{dt} = K[\frac{T_i+T_f}{2} -T_o]\)
Where Ti = initial temperature, Tf = final temperature, t is the time, and T0 = surrounding temperature.
\(\frac{Ti - T_f}{t} = K[\frac{T_i +T_f}{2} - T_o]\)
Calculation:
Given Ti = 70oC, Tf = 40oC, t = 5mins
\(\frac{70-40}{5} = K[\frac{70+40}{2} - 10]\)
6 = K × 45
K = 6/45
Applying the law of cooling in the second condition
\(\frac{50-20}{t} = K[\frac{50+20}{2} - 10]\)
\(\frac{30}{t} = \frac{6}{45}\times 25\)
\(t = \frac{30\times 45}{6\times 25}\) = 9 mins
t = 9 minute
Hence the correct option is 9 minute
Last updated on Jun 19, 2025
-> The AAI ATC Exam 2025 will be conducted on July 14, 2025 for Junior Executive..
-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025.
-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.
-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.
-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).
-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.
-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).
-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.
-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.