An ice cube with a mass of 20 g at -20 °C (typical freezer temperature) is dropped into a cup that holds 500 mL of hot water, initially at 83 °C. What is the final temperature in the cup? The density of liquid water is 1.00 g>mL; the specific heat capacity of ice is 2.03 J>g@C; the specific heat capacity of liquid water is 4.184 J>g@C; the enthalpy of fusion of water is 6.01 kJ>mol.

검증된 단계별 안내

Convert the mass of the ice cube to moles using the molar mass of water (18.015 g/mol).

Calculate the energy required to warm the ice from -20 °C to 0 °C using the specific heat capacity of ice (2.03 J/g°C).

Calculate the energy required to melt the ice at 0 °C using the enthalpy of fusion (6.01 kJ/mol).

Calculate the energy required to warm the melted ice (now water) from 0 °C to the final temperature using the specific heat capacity of liquid water (4.184 J/g°C).

Set up an energy balance equation where the heat lost by the hot water equals the total heat gained by the ice and solve for the final temperature.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

12m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It varies between different materials, influencing how they absorb and release heat. In this problem, the specific heat capacities of both ice and liquid water are crucial for calculating the heat transfer during the temperature change.

Enthalpy of Fusion

The enthalpy of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. For water, this value is significant when ice melts into liquid water, as it requires energy input, which affects the overall heat balance in the system.

Heat Transfer and Equilibrium

Heat transfer refers to the movement of thermal energy from a hotter object to a cooler one until thermal equilibrium is reached. In this scenario, the heat lost by the hot water will be equal to the heat gained by the ice, including the energy needed for melting. Understanding this principle is essential for determining the final temperature of the system.