A heated object (at time `t=0` and temperature `T=T_(0))` is taken out of the oven to cool and placed on a table near an open window Write an expression for its temperature as function of time `T` where `T_(s)` is the surrounding temperature .

If a piece of metal is heated to temperature theta and the allowed to cool in a room which is at temperature theta_0 , the graph between the temperature T of the metal and time t will be closet to

A rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as k= a//T , where a is a constant. The ends of the rod are kept at temperatures T_1 and T_2 . Find the function T(x), where x is the distance from the end whose temperature is T_1 .

Two identical objects A and B are at temperature T_(A) and T_(B) respectively. Both objects are placed in a room with perfectly absorbing walls maintained at temperature T(T_(A) gt T gt T_(B)) . Statement-1: The objects A and B attain the temperature T eventually Statement-2: A only emits radiation while B only absorbs until radiation both attain the temperature T

The graph shows the variation of l nR v//s (1)/(T^(2)) , where R is resistance and T is temperature. Then find R as function T .

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T_0 , while Box contains one mole of helium at temperature (7/3)T_0 . The boxes are then put into thermal contact with each other, and heat flows between them until the gasses reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gasses, T_f in terms of T_0 is

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) .

The resistance of an electrolyte varies with temperature T as R_(T) = (R_(O))/(1 + alpha T) , where R_(0) and are constants. A constant potential difference V is applied to the two electrodes (each of surface area A ) which are dipped in this electrolyte. If T_(0) is the temperature of the surroundings, the loss of heat to the surroundings per unit surface area put unit time is governed by the same relation H = k (T - T_(0)) A , the steady state temperature is