A metal ball of mass $1 \mathrm{~kg}$ is heated by means of a $20 \mathrm{~W}$ heater in a room at $20^{\circ} \mathrm{C}$ The temperature of the ball becomes steady at $50^{\circ} \mathrm{C}$.
(a) Find the rate of loss of heat to the surrounding when the ball is at $50^{\circ} \mathrm{C}$.
(b) Assuming Newton's law of cooling, calculating the rate of loss of heat to the surrounding when the ball is at $30^{\circ} \mathrm{C}$
(c) Assume that the temperature of the ball rises uniformly from $20^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ in 5 minutes. Find the total loss of heat to the surrounding during this period.
(d) Calculate the specific heat capacity of the metal.
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