Two substances A and B, initially at different temperatures, are thermally isolated from their surroundings and allowed to come into thermal contact. The mass of substance A is twice the mass of substance B, but the specific heat capacity of substance B is four times the specific heat capacity of substance A. Which substance will undergo a larger change in temperature?

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nicolaseobando nicolaseobando · Answer 1 · 2019-09-14T18:23:12+02:00

Answer:

B

Explanation:

For solving this we need a heat balance

[tex]Q_{a} = Q_{b}\\m_{a}*C_{a}*\Delta T_{a} = m_{b}*C_{b}*\Delta T_{b}[/tex]

By changing the corresponding relations, we have

[tex]m_{a}*C_{a}*\Delta T_{a} = \frac{1}{2}m_{a}*4C_{a}*\Delta T_{b} \\\\\\[/tex]

By cancelling similar factor, we obtain

[tex]\Delta T_{a} = 2 \Delta T_{b}\\\frac{\Delta T_{a}}{\Delta T_{b}} = 2\\[/tex]

Which means that the change of temperature in A is twice the change of B