Jaweria 2 years ago Please anyone help me!!

1. Jaweria

When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (a) What is the temperature of the drink after 50C minutes? (b) When will its temperature be 15°C?

2. Cha1234
3. chrismoon

@Cha1234 That question is asking for different values.

4. Jaweria

but this site has really confused answer

5. Jaweria

can anyone explain this to me here?

6. chrismoon

I learned this in basic physics, I assume solving the same way. Have you been taught Newton's Law of Cooling?$\frac{ dT }{ dt }=k(T-20)$

7. Jaweria

can anyone explain this to me that how I m getting this answer ln[(20 - T)/(20 - 5)] = - 0.01622

8. Jaweria

when I m calculating it I m getting 1.10623

9. satellite73

don't make it so hard it is easier than you think

10. satellite73

When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (a) What is the temperature of the drink after 50C minutes? (b) When will its temperature be 15°C?

11. satellite73

work with the differences in the temperature, that is what decays to zero initial difference is $$20-5=15$$ degrees, after 25 minutes the difference is $$10-20=10$$ degrees so the difference has decreased by $$\frac{10}{15}=\frac{2}{3}$$

12. satellite73

i.e. every 25 minutes, the difference in the temperature decreases by $$\frac{2}{3}$$ starting with an initial difference of $$15$$ you can model this by $15\left(\frac{2}{3}\right)^{\frac{t}{25}}$

13. satellite73

after another 25 minutes, at 50 minutes, it will decrease by another $$\frac{2}{3}$$ from $$10$$ to $$10\times \frac{2}{3}=\frac{20}{3}=6\tfrac{2}{3}$$

14. satellite73

that of course means it is $$6\tfrac{2}{3}$$ colder than the 20 degree room, so its temperature is $$20-6\tfrac{2}{3}=13\tfrac{1}{3}$$

15. satellite73

b) when will it be 15 degrees? that means b) when will it be 5 degrees colder than the room set $15\left(\frac{2}{3}\right)^{\frac{t}{25}}=5$ and solve for $$t$$