A metal block is taken from a furnace at and left to cool in a laboratory

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A metal block is taken from a furnace at

400^{\circ}\mathrm{C}

and left to cool in a laboratory. At the moment it is removed, the laboratory air temperature is

25^{\circ}\mathrm{C}

, but during the next half–hour the air-conditioning fails and the surrounding air slowly rises to

30^{\circ}\mathrm{C}

. However, during the first

12\,\text{min}

of cooling the laboratory air can be regarded as still constant at

25^{\circ}\mathrm{C}

. After

6\,\text{min}

the block is at

320^{\circ}\mathrm{C}

and after

12\,\text{min}

it is at

260^{\circ}\mathrm{C}

. (i) Treating the laboratory air temperature as

25^{\circ}\mathrm{C}

for these

12\,\text{min}

, form two simultaneous equations in the unknowns

k

and

T_s

and hence determine the values of

k

and the effective surrounding temperature

T_s

that best fit the readings. (ii) Using the values obtained, predict the temperature of the block at the instant

t=20\,\text{min}

after it was removed from the furnace, assuming the surrounding air has by then stabilised at

30^{\circ}\mathrm{C}

for all later times.