Paragraph (Q. 89-90): A system that can keep the room temperature within a narrow range between 2 0 ∘ C and 2 5 ∘ C includes a heat engine. When the room temperature drops lower than 2 0 ∘ C, the engi

Question

Paragraph (Q. 89-90): A system that can keep the room temperature within a narrow range between $2 0^{\circ}$ C and $2 5^{\circ}$ C includes a heat engine. When the room temperature drops lower than $2 0^{\circ}$ C, the engine turns on. When the temperature rises over $2 5^{\circ}$ C, the engine turns off. The room loses energy at a rate of $K (T - T_{0})$ , where $T_{0}$ is the outdoor temperature. The heat capacity of the room is $C$ . Given $T_{0} = 1 0^{\circ}$ C, $ln (\frac{3}{2}) = 0.4$ , $ln (\frac{6}{5}) = 0.18$ and $\frac{C}{K} = 750$ SI units. Suppose that at $t = 0$ the engine turns off. After how much time will the engine turn on again?

Options:

Answer:

B

Solution:

The room cools from $2 5^{\circ}$ C to $2 0^{\circ}$ C: $C \frac{d T}{d t} = - K (T - T_{0})$ . $t = \frac{C}{K} ln \frac{25 - 10}{20 - 10} = 750 \times ln 1.5 = 750 \times 0.4 = 300$ s = $5$ minutes. B.

TestHub · Accepted Answer

The room cools from 2 5 ∘ C to 2 0 ∘ C: C d t d T ​ = − K ( T − T 0 ​ ) . t = K C ​ ln 20 − 10 25 − 10 ​ = 750 × ln 1.5 = 750 × 0.4 = 300 s = 5 minutes. B.

Physics - Heat & Thermo Question with Solution | TestHub

Options:

Doubts & Discussion