Newton’s law of cooling

A liquid having mass m = 250 g is kept warm in a vessel by use of an electric heater. The liquid is maintained at 50^(@)C when the power supplied by heater is 30 watt and surrounding temperature is 20^(@)C . As the heater is switched off, the liquid starts cooling and it was observed that it took 10 second for temperature to fall down from 40^(@)C to 39.9^(@)C . Calculate the specific heat capacity of the liquid. Assume Newton’s law of cooling to be applicable.

A solid body A of mass m and specific heat capacity ‘s’ has temperature T_(1) = 400 K . It is placed, at time t = 0 , in atmosphere having temperature T_(0) = 300 K . It cools, following Newton’s law of cooling and its temperature was found to be T_(2) = 350 K at time t_(0) . At time t_(0) , the body A is connected to a large water bath maintained at atmospheric temperature T_(0) , using a conducting rod of length L, cross section A and thermal conductivity k. The cross sectional area A of the connecting rod is small compared to the overall surface area of body A. Find the temperature of A at time t = 2t_(0) .

Mass m of a liquid A is kept in a cup and it is at a temperature of 90^(@)C . When placed in a room having temperature of 20^(@)C , it takes 5 min for the temperature of the liquid to drop to 30^(@)C . Another liquid B has nearly same density as that of A and its sample of mass m kept in another identical cup at 50^(@)C takes 5 min for its temperature to fall to 30^(@)C when placed in room having temperature 20^(@)C . If the two liquids at 90^(@)C and 50^(@)C are mixed in a calorimeter where no heat is allowed to leak, find the final temperature of the mixture. Assume that Newton’s law of cooling is applicable for given temperature ranges.

Newton laws OF cooling

Explain Newton s laws of motion and show that (i) Newton s first law of motion defines force and (ii) Newton s second law of motion gives us the measure of force.

Consider the following statements. Kepler’s second law is based on the law of conservation of angular momentum. Kepler’s third law is based on Newton’s law of gravitation.

In accordance with Newton’s third law of motion -

Define the principle of conservation of linear momentum. Deduce the law of conservation of linear momentum from Newton’s third law of motion.

Assertion : Newton’s third law of motion is applicable only when bodies are in motion. Reason : Newton’s third law applies to all types of forces, e.g. gravitational, electric or magnetic forces etc.