Question

I place two substances, 1 and 2 in contact with each other so that they exchange heat with each other only, until they come to the same temperature. The mass of substance 1 is twice as much as the mass of substance 2. The temperature change for substance 2 is three times as much as the temperature change for substance 1. How does the specific heat of substance 2 compare to the specific heat of substance 1?

• A. The specific heat of substance 2 is 3/2 as much as the specific heat of substance 1.
• B. The specific heat of substance 2 is 2/3 as much as the specific heat of substance 1.
• C. The specific heat of substance 2 is bigger than the specific heat of substance 1, but we cannot determine how much bigger.
• D. The specific heat of substance 2 is smaller than the specific heat of substance 1, but we cannot determine how much smaller.
• E. We cannot determine how the specific heat of substance 2 is related to the specific heat of substance 1.

Answer 1

The correct option is B The specific heat of substance 2 is 2/3 as much as the specific heat of substance 1.

The heat lost be one substance is equal to the heat gained by other substance.

$⟹m_1{s}_1\Delta T_1=m_2{s}_2\Delta T_2$

$⟹\frac{s_2}{s_1}=\frac{m_1}{m_2}.\frac{\Delta T_1}{\Delta T_2}$

$=\frac{2}{1}.\frac{1}{3}=\frac{2}{3}$