Question

A lead fishing weight with a mass of 57g absorbs 146 cal of heat. If its initial temperature is 47 degrees Celsius, what is its final temperature?

Answer 1

The final temperature of the lead fishing weight after absorbing 146 cal of heat is calculated to be 132.38°C, using the specific heat capacity of lead and the formula for heat absorption.

Step-by-step explanation:

To calculate the final temperature of the lead fishing weight, we use the formula heat absorbed = mass × specific heat capacity × change in temperature (ΔT), or in algebraic terms: q = m × c × ΔT. We need to solve for ΔT by dividing the heat absorbed by the product of the mass and the specific heat capacity of lead. For lead, the specific heat is approximately 0.030 cal/g°C.

The formula will be rearranged to ΔT = q / (m × c). Plugging in the given values:

1. Calculate the change in temperature (ΔT): ΔT = 146 cal / (57 g × 0.030 cal/g°C) = 146 cal / 1.71 cal/°C = 85.38°C.
2. Add the change in temperature to the initial temperature to find the final temperature: Final Temperature = Initial Temperature + ΔT = 47°C + 85.38°C = 132.38°C.

Thus, the final temperature of the lead fishing weight would be 132.38°C after absorbing 146 cal of heat.

Answer 2

The heat and the corresponding difference in the temperature of the system can be related through the equation,
H = mcp(ΔT)
where H is heat, m is mass, cp is specific heat and equal to 1 cal/g°C for water, and ΔT is the temperature difference equal to T2 - T1. Substituting the known values,
146 cal = (57 g)(1 cal/ g°C)(T2 - 47°C)
The value of T2 from the equation is approximately 49.56°C.