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.

Newton's law of cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the (constant) temperature tau of the surrounding medium, we can write it as (dT)/(dt) = -k(T - tau) k gt 0 constant An cup of coffee is served at 185^(@)F in a room where the temperature is 65^(@)F . 2 minutes later the temperature of the coffee has dropped to 155^(@)F . log_(e)3 = 1.09872, log_(e).(3)/(4) = 0.2877 Temperature of coffee at time t is given by

Newton's law of cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the (constant) temperature tau of the surrounding medium, we can write it as (dT)/(dt) = -k(T - tau) k gt 0 constant An cup of coffee is served at 185^(@)F in a room where the temperature is 65^(@)F . 2 minutes later the temperature of the coffee has dropped to 155^(@)F . log_(e)3 = 1.09872, log_(e).(3)/(4) = 0.2877 Time required for coffee to have 105^(@)F temperature is

According to Newton's law, rate of cooling is proportional to the difference between the temperature of the body and the temperature of the air. If the temperature of the air is 20^(@)C and body cools for 20 min from 100^(@)C to 60^(@)C then the time it will take for it temperature to drop to 30^(@) is

A particular substance is being cooled by a stream of cold air (temperature of the air is constant and is 5^(@)C ) where rate of cooling is directly proportional to square of difference of temperature of the substance and the air. If the substance is cooled from 40^(@)C to 30^(@)C in 15 min and temperature after 1 hour is T^(@)C, then find the value of [T]//2, where [.] represents the greatest integer function.

The thermal radiation emitted by a body is proportional to T^(n) where T is its absolute temperature. The value of n is exactly 4 for

A sphere of density d , specific heat s and radius r is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure. If the temperature difference is DeltaT and surrounding temperature is T_(0) then rate of fall in temperature will be [Given that DeltaT lt lt T_(0) ]

A conductor has a temperature independent resistance R and a total heat capacity C . At the moment t=0 it is connected to a DC voltage V . Find the times dependence of the conductors temperature t assuming the thermal power dissipated into surrounding space to vary as q=k(T-T_0) where k is a constant T_0 is the surrounding temperature (equal to conductor's temperature at the initial moment).

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.

The specific heat of many solids at low temperatures varies with absolute temperature T according to the relation S=AT^(3) , where A is a constant. The heat energy required to raise the temperature of a mass m of such a solid from T = 0 to T = 20 K is

A body with an initial temperature theta_(1) is allowed to cool in a surrounding which is at a constant temperature of theta_(0) (theta lt theta_(1)) Assume that Newton's law of cooling is obeyed Let k = constant The temperature of the body after time t is best experssed by .