(TEMPERATURE CHANGE) The rate at which the temperature of an object changes is proportional to the difference between its own temperature and the temperature of the surrounding medium. Express this rate as a function of the temperature of the object
dT/dt = k (Tmedium - Town)
the percent of decrease of temperature at noon 24f but now its 8f
Tha temperature at 6 p.m. Was 16 f, which was 9 f lower than the temperature at noon. What was the temperature at noon
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At 9:00 AM, the temperature is 14°C. If the temperature drops 4°C per hour, what will the temperature be at 11:00 AM?
This morning was 80 decrease outside the Temperature increased 12 degrees what is the temperature now
At 7 AM the air was cool but by noon the temperature had increased 25° to 68 Fahrenheit what was the temperature at 7 AM
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To express the rate at which the temperature of an object changes, we can use the concept of differential equations. Let's denote the rate of temperature change as dT/dt, which represents the derivative of the temperature with respect to time.
According to the given information, the rate of temperature change is proportional to the difference between the object's temperature and the temperature of the surrounding medium. Let's denote the object's temperature as T(t) and the temperature of the surrounding medium as Ts.
Now, we can express the rate of temperature change using the proportional relationship as:
dT/dt = k(T - Ts)
Here, k is the constant of proportionality. This equation represents the rate at which the object's temperature changes with time. The temperature difference (T - Ts) determines the direction and magnitude of the change, while the constant k determines the rate of change.
To solve this equation, one needs to have initial conditions or additional information, such as the value of T(t) at a specific time or the value of Ts. By providing these conditions, it is possible to find a particular solution for the temperature function T(t) using standard methods for solving differential equations.