A block of metal is heated to a temperature much higher than the room temperature and placed in an evacuated cavity. The curve which correctly represents the rate of cooling ( T is temperature of the block and t is the time.)

Step-by-step solution

Key Idea Newton's law of cooling is given by expression, - d T d t =k^ (T-T₀ ) where, k^ = k m s and negative sign shows the rate of heat loss. The given expression can be rearranged by integrating as, d T T-T₀ =-k^ d t array rlrl _e (T-T₀ ) & =-k^ t+ _e A ( _e A= Constant ) & - d T (T-T₀ ) & =k^ d t & (T-T₀ ) & =-k^ t & & T & =e^ -k^ t +T₀ at t & & T & =T₀ , at t=0 T array Hence, the graph as shown below, shows temperature of a body (done) varies exponentially with time from T to T₀ (T₀ Thus, the correct option is