Home
Class 12
MATHS
A body at a temperature of 50^0F is plac...

A body at a temperature of `50^0F` is placed outdoors where the temperature is `100^0F` . If the rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium. If after 5 min the temperature of the body is `60^0F` , find (a) how long it will take the body to reach a temperature of `75 ^0` F and (b) the temperature of the body after 20 min.

Text Solution

AI Generated Solution

To solve the problem, we will follow these steps: ### Step 1: Set up the differential equation We know that the rate of change of the temperature of the body is proportional to the temperature difference between the body and its surrounding medium. Let: - \( T(t) \) be the temperature of the body at time \( t \). - \( T_0 = 100^\circ F \) be the surrounding temperature. The differential equation can be expressed as: ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise EXAMPLES|18 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISES 10.1|6 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

When the temperature of a body increases

Derive Newton's law of cooling to show that the rate of loss of heat from the body is proportional to the temperature difference between the body and its surroundings.

A solid at temperature T_(1) is kept in an evacuated chamber at temperature T_(2)gtT_(1) . The rate of increase of temperature of the body is propertional to

Write down the body temperature of a healthy person.

Calculate the temperature of the black body from given graph.

Name the instrument used to measure the temperature of a body.

Human body temperature is maintained by

if temperature of an object is 140^(@)F , then its temperature in centigrade is

The temperature T of a cooling object drops at a rate proportional to the difference T - S where S is constant temperature of surrounding medium. If initially T = 150^@C ; find the temperature of the cooling object at any time t.

The energy that is transferred from a body at a higher temperature to a body at a lower temperature