You are taking a road trip in a car without A/C. The temperture in the car is 85 degrees F. You buy a cold pop at a gas station. Its initial temperature is 45 degrees F. The pop's temperature reaches 60 degrees F after 47 minutes. Given that T-A -kt To-A where T the temperature of the pop at time t. To the initial temperature of the pop. A= the temperature in the car. k=a constant that corresponds to the warming rate. and t the length of time that the pop has been warming up. How long will it take the pop to reach a temperature of 79.75 degrees F? minutes. It will take
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![**Scenario**: You are taking a road trip in a car without A/C. The temperature in the car is 85 degrees F. You buy a cold pop at a gas station. Its initial temperature is 45 degrees F. The pop's temperature reaches 60 degrees F after 47 minutes.
**Given**:
\[
\frac{T - A}{T_0 - A} = e^{kt}
\]
where:
- \( T \) = the temperature of the pop at time \( t \).
- \( T_0 \) = the initial temperature of the pop.
- \( A \) = the temperature in the car.
- \( k \) = a constant that corresponds to the warming rate.
- \( t \) = the length of time that the pop has been warming up.
**Question**: How long will it take the pop to reach a temperature of 79.75 degrees F?
**It will take \(\underline{\hspace{2cm}}\) minutes.**
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This equation describes the warming of the pop over time using an exponential model. The constant \( k \) indicates how quickly the temperature equilibrates with the car temperature. Solving for \( t \) when the pop reaches 79.75 degrees F involves substituting the known values into the equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74679fe8-edb8-480a-bbc2-dbd98253ae77%2F80f6cbd4-d1be-48af-b575-b2030028fd8b%2Fofo77m_processed.jpeg&w=3840&q=75)
![Oil leaks from a tank. At hour \( t = 0 \) there are 230 gallons of oil in the tank. Each hour after that, 6% of the oil leaks out.
(a) What percent of the original 230 gallons has leaked out after 11 hours?
\[ \_\_\% \]
(b) If \( Q(t) = Q_0 e^{kt} \) is the quantity of oil remaining after \( t \) hours, find the value of \( k \).
\[ k = \_\_ \]
(c) What does \( k \) tell you about the leaking oil? Select all that apply if more than one statement is true.
- □ A. It tells by what percent of oil decays each hour.
- □ B. It tells what percent of oil remains after each hour.
- □ C. It is the amount that the oil that leaks out each second.
- □ D. Because it is less than one, we know the amount of oil in the tank is decreasing.
- □ E. Because it is negative, we know the amount of oil in the tank is decreasing.
- □ F. It gives the continuous hourly rate at which oil is leaking.
- □ G. None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74679fe8-edb8-480a-bbc2-dbd98253ae77%2F80f6cbd4-d1be-48af-b575-b2030028fd8b%2Ftgjsbxp_processed.jpeg&w=3840&q=75)
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