The temperature T of a cooling object drops at a rate proportional to the difference T-S, where S is the constant temperature of the surrounding medium. Thus, `(dT)/(dt)=-k(T-S)`, where k(>0) is constant and t is the time. Solve the differntial equation if it is given that T(0)=150.

The temperature T of a cooling drops at a rate proportional to the difference T-S, where S is the constant temperature of surrounding medium. A thermometer reading 80^@F was taken outside. Five minutes later, the thermometer read 60^@F . After another five minutes the reading was 50^@F . what was the outside temperature?

The unit of 1 s t order rate constant are

If d varies directly as t^(2) then dt^(2)=k where k is some constant ?

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation (d V(t))/(dt) =-k(T-t) , where k"">""0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is : (1) T^2-1/k (2) I-(k T^2)/2 (3) I-(k(T-t)^2)/2 (4) e^(-k T)

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.

For the ideal gaseous reaction, the rate is generally expressed in terms of (dP)/(dt) instead of (dC)/(dt) or (dn)/(dt) (where C= (n)/(V) is concentration and n the no. of moles). What is the relation among these three expressions if T and V are constant?

An object is covering distance in direct proporiton to t^3 , where t is the time elapsed. What conclusions might you draw about the acceleration ? Is it constant or increasing or decreasing or zero?

If the rate constant for a first order reaction is k, the time (t) required for completion of 99 % of the reaction is given by

The time t of a complete oscillation of a simple pendulum of length l is given by the equation T=2pisqrt(1/g) where g is constant. What is the percentage error in T when l is increased by 1%? Comment the above result.