Calorimeter Homework: Clock Period & Temperature Change

• mimi83
In summary, a clock with a simple pendulum designed to have a period of one second at 20.0°C will run either fast or slow when operated at a constant temperature of -80.0°C. The number of periods the pendulum will go through before the clock is off by 1.00 s can be calculated using the rule of thumb for pendulum length, taking into account the coefficient of linear expansion of aluminum.
mimi83

Homework Statement

A clock is designed with a simple pendulum, consisting of a mass at the end of an aluminum rod, whose period is supposed to be equal to one second. The clock is designed to keep accurate time at 20.0°C, but is operated at a constant temperature of −80.0°C. (a) Will the clock run fast or slow? Explain. (b) How many periods will the pendulum go through before the clock is off by 1.00 s? (The coefficient of linear expansion of aluminum is 2.31×10−5 1/C°.)

Q = cmΔT
Qw + Qo = 0
ΔL = LiαΔT

The Attempt at a Solution

you

I would like to first clarify that the equations you have provided are related to calorimetry, which deals with the measurement of heat and temperature changes. However, in this scenario, we are dealing with a clock and its accuracy, which is not directly related to heat and temperature changes.

To solve this problem, we need to consider the effects of temperature on the period of a pendulum. The period of a pendulum is directly proportional to the square root of its length and inversely proportional to the square root of the acceleration due to gravity. However, temperature can also affect the length of the pendulum due to thermal expansion.

(a) In this scenario, the clock is operated at a temperature much lower than its designed temperature. As a result, the aluminum rod will contract due to thermal contraction, causing the pendulum to become shorter. This will result in a shorter period of oscillation, meaning the clock will run faster at -80.0°C compared to 20.0°C.

(b) To calculate the number of periods that the pendulum will go through before the clock is off by 1.00 s, we need to use the equation:

ΔT = (ΔL/Li) * (1/α)

Where ΔT is the change in temperature, ΔL is the change in length, Li is the initial length of the pendulum, and α is the coefficient of thermal expansion of aluminum.

We know that the clock is off by 1.00 s, which means the period of the pendulum has changed by 1.00 s. We also know that the coefficient of thermal expansion of aluminum is 2.31×10−5 1/C°. Therefore, we can rearrange the equation to solve for ΔL:

ΔL = (ΔT * α * Li)

Substituting the values, we get:

ΔL = (1.00 s * 2.31×10−5 1/C° * 1 m) = 2.31×10−5 m

This means that the pendulum has shortened by 2.31×10−5 m at -80.0°C. Now, we can use the equation for the period of a pendulum to calculate the number of periods:

T = 2π * √(L/g)

Where T is the period, L is the length of the pendulum, and g is

1. What is a calorimeter and how does it work?

A calorimeter is a device used to measure the amount of heat absorbed or released in a chemical reaction. It works by using a thermometer to measure the change in temperature of a substance before and after a reaction. The heat released or absorbed can then be calculated using the specific heat capacity of the substance.

2. How is a calorimeter used to determine the heat of a reaction?

A calorimeter is used to determine the heat of a reaction by measuring the change in temperature of the reaction mixture. The heat released or absorbed by the reaction can be calculated using the formula Q = m*c*ΔT, where Q is the heat released or absorbed, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

3. What is clock period and how is it related to temperature change in a calorimeter?

Clock period is the time it takes for a chemical reaction to reach completion. In a calorimeter, the clock period is related to temperature change because the longer the reaction takes, the more heat is released or absorbed, resulting in a larger change in temperature.

4. How does the specific heat capacity affect the accuracy of a calorimeter?

The specific heat capacity is a measure of how much heat a substance can absorb or release. In a calorimeter, a higher specific heat capacity can lead to a more accurate measurement of heat because it can absorb or release more heat without significantly changing its temperature. Therefore, using a substance with a higher specific heat capacity can result in a more precise measurement of the heat of a reaction.

5. Can a calorimeter be used to measure the heat of any reaction?

While a calorimeter can be used to measure the heat of many reactions, it may not be suitable for all reactions. Some reactions may produce too much heat, resulting in a significant change in temperature that is difficult to measure accurately. In these cases, alternative methods may need to be used to determine the heat of the reaction.

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