getinthere
New member
- Joined
- Oct 26, 2014
- Messages
- 8
Hi,
I have been given a question involving calculus, I have answered this question as I feel is correct, but would like someone to verify this and point out any errors I may have made.
The question:
When a heated object is cooling down, the rate of change of the object’s internal temperature T(t) is proportional to S (t) -T(t), where S (t) is the temperature of the surroundings in which the object is immersed.
a) Form a differential equation that describes the situation above, using k for the constant of proportionality.
A ball made from a specialised metal alloy is being tested to determine some of its material properties. As part of the test, the ball is heated throughout to 200°C and then immediately immersed into a large pool of temperature controlled water, Whose temperature obeys the formula S(t) = 15e^-5t + 5. For this specific ball, k = 0.5. Let t by the time in hours after the ball has started to cool down, so that T(0) = 200.
b) Solve the differential equation in part (a) to iind the particular solution T(t).
My answer is attached, thank you.
John
I have been given a question involving calculus, I have answered this question as I feel is correct, but would like someone to verify this and point out any errors I may have made.
The question:
When a heated object is cooling down, the rate of change of the object’s internal temperature T(t) is proportional to S (t) -T(t), where S (t) is the temperature of the surroundings in which the object is immersed.
a) Form a differential equation that describes the situation above, using k for the constant of proportionality.
A ball made from a specialised metal alloy is being tested to determine some of its material properties. As part of the test, the ball is heated throughout to 200°C and then immediately immersed into a large pool of temperature controlled water, Whose temperature obeys the formula S(t) = 15e^-5t + 5. For this specific ball, k = 0.5. Let t by the time in hours after the ball has started to cool down, so that T(0) = 200.
b) Solve the differential equation in part (a) to iind the particular solution T(t).
My answer is attached, thank you.
John