A block of ice initially at 0 °C is transferred to a warm laboratory where the air…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A block of ice initially at 0 °C is transferred to a warm laboratory where the air temperature is maintained at 25 °C. Let θ(t) denote the temperature of the block (in °C) after t minutes.
(i) Set up and solve the differential equation governing θ(t), taking θ(0)=0.
(ii) Show that the time taken for the ice to warm from 0 °C to 12.5 °C is exactly the same as the time taken to warm from 12.5 °C to 18.75 °C.
(iii) Obtain an expression for the time required for θ(t) to rise from 0 °C to an arbitrary temperature θ1\,(0<θ1<25). Hence, determine the time needed for the block to reach 24 °C.