/*! 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 120 As fresh-poured concrete hardens... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 120

As fresh-poured concrete hardens, the chemical transformation releases energy at a rate of \(2 \mathrm{~W} / \mathrm{kg}\). Assume that the center of a poured layer does have a heat loss of \(0.3 \mathrm{~W} / \mathrm{kg}\) and that it has an average specific heat of \(0.9 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\). Find the temperature rise during \(3 \mathrm{~h}\) of the hardening (curing) process.

Short Answer

Expert verified
The temperature rises by 20.4 K after 3 hours.

Step by step solution

01

Determine Net Heat Production

First, calculate the net heat production per kilogram of concrete. The rate of heat production due to the chemical process is given as \( 2 \mathrm{~W} / \mathrm{kg} \). The heat loss is \( 0.3 \mathrm{~W} / \mathrm{kg} \). Therefore, the net heat production is: \[\text{Net Heat Production} = 2 \mathrm{~W} / \mathrm{kg} - 0.3 \mathrm{~W} / \mathrm{kg} = 1.7 \mathrm{~W} / \mathrm{kg}\]
02

Calculate Total Energy Produced in 3 Hours

Next, find out how much energy is produced per kilogram in 3 hours. Since we calculated the net heat production per unit time, multiply this by the time in seconds (since power is in Watts, \(1 \mathrm{~W} = 1 \mathrm{~J/s}\)). First convert hours to seconds:\[3 \mathrm{~hours} = 3 \times 60 \times 60 \mathrm{~s} = 10800 \mathrm{~s}\]Then, calculate the total energy:\[\text{Total Energy} = 1.7 \mathrm{~W} / \mathrm{kg} \times 10800 \mathrm{~s} = 18360 \mathrm{~J} / \mathrm{kg}\]
03

Use Specific Heat to Find Temperature Rise

Finally, use the given specific heat capacity to determine the temperature rise for the concrete. The formula relating energy, specific heat capacity, mass, and temperature change is:\[\Delta T = \frac{Q}{m \cdot c}\]where \( Q \) is the total heat energy, \( m \) is the mass (in this case, per 1 kg, hence the terms cancel), and \( c \) is the specific heat capacity.Convert specific heat to \( \mathrm{J/kg \cdot K} \):\[c = 0.9 \mathrm{~kJ/kg \cdot K} = 900 \mathrm{~J/kg \cdot K}\]Calculate temperature rise:\[\Delta T = \frac{18360 \mathrm{~J/kg}}{900 \mathrm{~J/kg \cdot K}} = 20.4 \mathrm{~K}\]
04

Conclusion: Final Temperature Increase

The temperature of the concrete rises by \( 20.4 \mathrm{~K} \) during the 3 hours of hardening.

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Key Concepts

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

Heat Transfer
Heat transfer refers to the movement of thermal energy from one object or material to another. This process can happen through various mechanisms including conduction, convection, and radiation. In the context of this exercise, as the concrete sets, heat is generated from a chemical reaction within the material itself.

The exercise illustrates both the production and loss of heat. Concrete releases energy at a rate of 2 W/kg due to the hardening process. However, not all this heat remains in the concrete; some of it is lost, in this case at a rate of 0.3 W/kg.

The net heat transfer, which affects the rise in temperature, is calculated by subtracting the heat lost from the heat produced. This net value tells us how much energy is ultimately available to raise the concrete鈥檚 temperature during the curing process.
Specific Heat Capacity
Specific heat capacity is a property of a material that describes the amount of heat required to change its temperature by one degree Kelvin or Celsius. It is a critical factor in understanding how a substance like concrete reacts to added or removed thermal energy.

In this problem, concrete has a specific heat capacity of 0.9 kJ/kg-K. Converted to standard units, this is 900 J/kg-K.

This means that 900 Joules of energy are needed to raise the temperature of one kilogram of concrete by one Kelvin. By using this specific heat value, we can determine how the concrete will respond to the thermal energy produced in the hardening process.
Thermal Energy
Thermal energy is the energy that comes from the temperature of the heated substance. It's the total energy of all the particles in an object due to their random motion. The chemical process in concrete releases thermal energy.

In this exercise, we calculate how much total thermal energy is generated over a 3-hour period. Given the net heat production per kilogram, which is 1.7 W/kg after accounting for losses, this value is multiplied by time to find the total energy generated: 18360 J/kg.

The thermal energy, calculated in Joules, is then used along with the specific heat capacity to determine the change in temperature of the concrete. Understanding the concept of thermal energy is essential for knowing how various substances react to heat.

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Most popular questions from this chapter

A cylinder fitted with a frictionless piston contains R-134a at \(100 \mathrm{~F}, 80 \%\) quality, at which point the volume is 3 gal. The external force on the piston is now varied in such a manner that the R-134a slowly expands in a polytropic process to \(50 \mathrm{lbf} / \mathrm{in} .^{2}, 80 \mathrm{~F}\). Calculate the work and the heat transfer for this process.

Refrigerant-410A in a piston/cylinder arrangement is initially at \(60 \mathrm{~F}, x=1\). It is then expanded in a process so that \(P=C v^{-1}\) to a pressure of 30 \(\mathrm{lbf} / \mathrm{in} .^{2}\). Find the final temperature and specific volume.

Determine whether refrigerant R-410A in each of the following states is a compressed liquid, a superheated vapor, or a mixture of saturated liquid and vapor. a. \(50^{\circ} \mathrm{C}, 0.005 \mathrm{~m}^{3} / \mathrm{kg}\) b. \(1.0 \mathrm{MPa}, 5^{\circ} \mathrm{C}\) c. \(0.1 \mathrm{MPa}, 0.1 \mathrm{~m}^{3} / \mathrm{kg}\) d. \(-20^{\circ} \mathrm{C}, 200 \mathrm{kPa}\)

A rigid tank of \(1 \mathrm{~m}^{3}\) contains nitrogen gas at \(600 \mathrm{kPa}, 400 \mathrm{~K}\). By mistake, someone lets \(0.6 \mathrm{~kg}\) flow out. If the final temperature is \(380 \mathrm{~K}\), what is the final pressure?

A container is split in two equal volumes by a stiff membrane. One part is evacuated and the other part has \(1 \mathrm{lbm}\) R-410A at 100 psia, \(140 \mathrm{~F}\). Now the membrane ruptures and the system comes to equilibrium at \(100 \mathrm{~F}\) by some heat transfer. Find the heat transfer and the final pressure.
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