An unknown mass of each substance, initially at 23.0 °C, absorbs 1.95 × 10³ J of heat. The final temperature is recorded. Find the mass of each substance.
a. Pyrex glass (T_f = 55.4°C)
b. sand (T_f = 62.1°C)
c. ethanol (T_f = 44.2°C)
d. water (T_f = 32.4°C)

검증된 단계별 안내

Identify the specific heat capacity of Pyrex glass, which is typically around 0.75 J/g°C.

Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat absorbed, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Calculate the change in temperature \( \Delta T \) using the initial and final temperatures: \( \Delta T = T_f - T_i = 55.4 \text{ °C} - 23.0 \text{ °C} \).

Rearrange the formula to solve for mass \( m \): \( m = \frac{q}{c \cdot \Delta T} \).

Substitute the known values into the rearranged formula: \( q = 1.95 \times 10^3 \text{ J} \), \( c = 0.75 \text{ J/g°C} \), and \( \Delta T \) calculated in the previous step, to find the mass \( m \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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 for different materials and is crucial for calculating temperature changes when heat is absorbed or released. In this problem, knowing the specific heat capacity of Pyrex glass allows us to relate the heat absorbed to the change in temperature and ultimately find the mass.

Heat Transfer Equation

The heat transfer equation, often expressed as Q = mcΔT, relates the heat absorbed or released (Q) to the mass (m), specific heat capacity (c), and the change in temperature (ΔT). This equation is fundamental in thermodynamics and is used to solve for unknown variables, such as mass, when heat transfer is involved. In this case, it will help determine the mass of the Pyrex glass based on the heat absorbed and the temperature change.

Temperature Change

Temperature change (ΔT) is the difference between the final temperature (Tf) and the initial temperature (Ti) of a substance. It is a critical factor in thermodynamic calculations, as it directly influences the amount of heat absorbed or released. In this scenario, the temperature change of the Pyrex glass from 23.0 °C to 55.4 °C is essential for applying the heat transfer equation to find the mass of the substance.

An unknown mass of each substance, initially at 23.0 °C, absorbs 1.95 × 103 J of heat. The final temperature is recorded. Find the mass of each substance.a. Pyrex glass (Tf = 55.4°C)b. sand (Tf = 62.1°C)c. ethanol (Tf = 44.2°C)d. water (Tf = 32.4°C)