Two containers A and B are connected by a conducting solid cylindrical rod of length 242 7 ~cm and radius 8.3 ~cm . Thermal conductivity of the rod is 693 watt/mole-K. The container A contains two mole of oxygen gas and the container B contains four mole of helium gas. At time t=0 temperature difference of the containers is 50^ C , after what time (in seconds) temperature difference between them will be 25^ C . Trans

Step-by-step solution

Thermal resistance of the rod, R = kA When heat is transferred from first vessel to second, temperature of first vessel decreases while that of second vessel increases. Due to both there reasons, difference between temperature of vessels decreases. Let at an instant t , the temperature difference between two vessels be . H= R = K A dQ = Hdt = KA dt ....(i) Since gases are contained in two vessels, therefore, processes on gases in two vessels are isochoric. Hence, decrease in temperature of gas in first vessel, ₁= d