/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 A technician measures the specif... [FREE SOLUTION] | 91Ó°ÊÓ

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A technician measures the specific heat of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat, which is then transferred to the liquid for \(120 \mathrm{~s}\) at a constant rate of \(65.0 \mathrm{~W}\). The mass of the liquid is \(0.780 \mathrm{~kg},\) and its temperature increases from \(18.55^{\circ} \mathrm{C}\) to \(22.54^{\circ} \mathrm{C}\). (a) Find the average specific heat of the liquid in this temperature range. Assume that negligible heat is transferred to the container that holds the liquid and that no heat is lost to the surroundings. (b) Suppose that in this experiment heat transfer from the liquid to the container or its surroundings cannot be ignored. Is the result calculated in part (a) an overestimate or an underestimate of the average specific heat? Explain.

Short Answer

Expert verified
(a) The specific heat is approximately 2610.77 J/(kg·°C). (b) It's an underestimate due to unaccounted heat loss.

Step by step solution

01

Calculate the total energy supplied

The electrical power supplied is given by \( P = 65.0 \, \text{W} \). The power is supplied for a time \( t = 120 \, \text{s} \). Therefore, the total energy \( Q \) transferred to the liquid is calculated as follows:\[ Q = P \times t = 65.0 \, \text{W} \times 120 \, \text{s} = 7800 \, \text{J} \]
02

Calculate the temperature change of the liquid

The initial and final temperatures of the liquid are \( T_i = 18.55^{\circ} \text{C} \) and \( T_f = 22.54^{\circ} \text{C} \) respectively. Therefore, the change in temperature \( \Delta T \) is:\[ \Delta T = T_f - T_i = 22.54 - 18.55 = 3.99^{\circ} \text{C} \]
03

Calculate the specific heat capacity

The specific heat capacity \( c \) can be calculated using the formula:\[ Q = m \cdot c \cdot \Delta T \]Where:- \( m = 0.780 \, \text{kg} \) (mass of the liquid)- \( \Delta T = 3.99^{\circ} \text{C} \) (temperature change)Rearranging for \( c \):\[ c = \frac{Q}{m \cdot \Delta T} = \frac{7800 \, \text{J}}{0.780 \, \text{kg} \times 3.99^{\circ} \text{C}} \approx 2610.77 \, \text{J/(kg} \cdot \text{°C)} \]
04

Analyze possible heat losses

If heat transfer from the liquid to the container or its surroundings is considered, the calculated specific heat would be an underestimate. This is because some of the energy would dissipate into the surroundings instead of transferring into the liquid, leading to a higher energy requirement to achieve the measured temperature change.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat Transfer
Heat transfer is a fundamental concept in physics and refers to the movement of thermal energy from one object or medium to another. In the experiment described, heat transfer occurs when the energy generated by the electrical resistor is transferred to the liquid. This transfer of energy causes the liquid's temperature to rise.

It is crucial to understand that heat transfer can happen via three main mechanisms:
  • Conduction: Direct transfer of heat through a material.
  • Convection: Transfer of heat through a fluid, including gases and liquids, by the movement of the fluid itself.
  • Radiation: Transfer of heat through electromagnetic waves.
In our case, it's a form of conduction and possibly convection as the heat generated in the resistor spreads through the liquid. The efficiency of heat transfer directly influences the effectiveness of energy use in various applications, including cooking, heating systems, and industrial processes.
Energy Conversion
Energy conversion is the process of transforming energy from one form to another. In the context of this experiment, electrical energy from the resistor is converted into thermal energy or heat. This is a common phenomenon where energy in the form of electricity is used to produce heat, as seen in devices like electric stoves and water heaters.

This conversion is pivotal when calculating the energy supplied to a system. The power of the resistor, given in watts (a unit of power equivalent to joules per second), helps calculate the total energy converted to heat over a specific duration. It is important to note that during energy conversion, some energy might be lost to the surroundings, becoming important in determining the experiment's efficiency. Special attention must be paid to ensure that all energy conversions are accounted for, as any unacknowledged energy loss can lead to errors in calculations, affecting factors such as the specific heat capacities of substances involved.
Temperature Change
Temperature change is a measure of how much the thermal energy of a substance has increased or decreased. In the described experiment, the identification of temperature change allows us to compute the specific heat capacity of the unknown liquid.

The change in temperature (\( \Delta T \)) is calculated simply by subtracting the initial temperature from the final temperature. This simple but crucial calculation is essential as it helps us understand how the liquid absorbs heat. If the temperature of the liquid increases significantly with a small amount of heat, it indicates a low specific heat capacity. Conversely, a large amount of energy causing only a small change in temperature signifies a high specific heat capacity.Temperature change can be affected by surrounding conditions, emphasizing the need for careful control of heat loss during experiments. Variations can lead to inaccurate specific heat capacity readings in practical applications.
Experimental Physics
Experimental physics involves the practical side of analyzing and understanding the laws of physics through experimentation and observation. The scenario in this task represents a classic type of laboratory experiment aimed at measuring specific heat capacity.

In experimental physics, controlling variables is essential. Assumptions like negligible heat loss to the container or environment simplify calculations but may not always reflect real-world conditions.
  • Errors can occur from external heat transfer.
  • Precision instruments are critical to reliable experiments.
  • Repeatability and documentation are vital for validating results.
This particular exercise teaches how to account for stray forms of energy loss and consider their impact on experimental outcomes. The importance of conducting such rigorous experiments ensures that theoretical predictions hold when applied to practical situations, advancing our technological and scientific capabilities.

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Most popular questions from this chapter

You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is \(28.4 \mathrm{~N}\). You carefully add \(1.25 \times 10^{4} \mathrm{~J}\) of heat energy to the sample and find that its temperature rises \(18.0 \mathrm{C}^{\circ} .\) What is the sample's specific heat?

A carpenter builds an exterior house wall with a layer of wood \(3.0 \mathrm{~cm}\) thick on the outside and a layer of Styrofoam insulation \(2.2 \mathrm{~cm}\) thick on the inside wall surface. The wood has a thermal conductivity of \(0.080 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}),\) and the Styrofoam has a thermal conductivity of \(0.010 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})\). The interior surface temperature is \(19.0^{\circ} \mathrm{C}\). and the exterior surface temperature is \(-10.0^{\circ} \mathrm{C}\). (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a \(200.0 \mathrm{~W}\) electric immersion heater in \(0.320 \mathrm{~kg}\) of water. (a) How much heat must be added to the water to raise its temperature from \(20.0^{\circ} \mathrm{C}\) to \(80.0^{\circ} \mathrm{C} ?\) (b) How much time is required if all of the heater's power goes into heating the water?

An \(8.50 \mathrm{~kg}\) block of ice at \(0^{\circ} \mathrm{C}\) is sliding on a rough horizontal icehouse floor (also at \(0^{\circ} \mathrm{C}\) ) at \(15.0 \mathrm{~m} / \mathrm{s}\). Assume that half of any heat generated goes into the floor and the rest goes into the ice. (a) How much ice melts after the speed of the ice has been reduced to \(10.0 \mathrm{~m} / \mathrm{s} ?\) (b) What is the maximum amount of ice that will melt?

You have no doubt noticed that you usually shiver when you get out of the shower. Shivering is the body's way of generating heat to restore its internal temperature to the normal \(37^{\circ} \mathrm{C}\). and it produces approximately \(290 \mathrm{~W}\) of heat power per square meter of body area. A \(68 \mathrm{~kg}(150 \mathrm{lb}), 1.78 \mathrm{~m}(5 \mathrm{ft}, 10\) in.) person has approximately \(1.8 \mathrm{~m}^{2}\) of surface area. How long would this person have to shiver to raise his or her body temperature by \(1.0 \mathrm{C}^{\circ},\) assuming that none of this heat is lost by the body? The specific heat of the body is about \(3500 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K}).\)

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