The problem states that there are two identical crucibles containing equal masses of silver and gold. According to the table, find the ratio of the heating time of silver to the heating time of gold at the same temperature, if the power of the furnaces is the same and heat loss is negligible. Round the answer to the nearest tenth.

Solution:

The problem asks for the ratio of heating times of silver and gold. We are given that the crucibles are identical, the masses of silver and gold are equal, the final temperature is the same, and heat loss is negligible. The power of the furnaces is also the same, which means the rate of heat transfer is the same for both substances.

The amount of heat required to raise the temperature of a substance is given by the formula:

\[ Q = mc \Delta T \]

where:

• Q is the heat energy transferred
• m is the mass of the substance
• c is the specific heat capacity of the substance
• ΔT is the change in temperature

The rate of heat transfer is given by P = Q / t, where P is the power and t is the time. Since the power of the furnaces is the same, we have:

\[ P = \frac{m_s c_s \Delta T}{t_s} = \frac{m_g c_g \Delta T}{t_g} \]

We are given that $$m_s = m_g$$ (equal masses) and $$\Delta T_s = \Delta T_g$$ (same temperature change). Therefore, we can simplify the equation to:

\[ \frac{c_s}{t_s} = \frac{c_g}{t_g} \]

We need to find the ratio $$t_s / t_g$$. Rearranging the equation, we get:

\[ \frac{t_s}{t_g} = \frac{c_s}{c_g} \]

Now, we need to find the specific heat capacities of silver and gold from the provided table. The table provides 'Удельная теплоемкость, Дж/(кг·°C)', which is the specific heat capacity.

From the table:

• Specific heat capacity of silver (серебро) = 250 Дж/(кг·°C)
• Specific heat capacity of gold (золото) = 130 Дж/(кг·°C)

Now we can calculate the ratio of heating times:

\[ \frac{t_s}{t_g} = \frac{c_s}{c_g} = \frac{250}{130} \]

\[ \frac{t_s}{t_g} \approx 1.923 \]

Rounding the answer to the nearest tenth, we get 1.9.