A system S receives heat continuously from an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to Newton's law of cooling, the rate of heat loss is $\frac{dQ}{dt} = k(T - T_{surr})$.When the temperature is constant at $50^{\circ}C$

Vedclass · Accepted Answer

$1500$

Vedclass · Answer

(D) According to Newton's law of cooling, the rate of heat loss is $\frac{dQ}{dt} = k(T - T_{surr})$.When the temperature is constant at $50^{\circ}C$, the heat supplied equals the heat lost: $10 = k(50 - 20) = 30k$. Thus, $k = \frac{1}{3} \ W/^{\circ}C$.When the heater is switched off, the system cools. The average temperature during the cooling interval is $T_{avg} = \frac{35.1 + 34.9}{2} = 35^{\circ}C$.The rate of heat loss at this average temperature is $\frac{dQ}{dt} = k(T_{avg} - T_{surr}) = \frac{1}{3}(35 - 20) = \frac{15}{3} = 5 \ J/s$.In $1 \ minute$ $(60 \ seconds)$, the total heat lost is $Q = 5 \ J/s 	imes 60 \ s = 300 \ J$.The change in temperature is $\Delta T = 35.1^{\circ}C - 34.9^{\circ}C = 0.2^{\circ}C$.The heat capacity $C$ is given by $C = \frac{Q}{\Delta T} = \frac{300 \ J}{0.2^{\circ}C} = 1500 \ J/^{\circ}C$.

Similar Questions

$A$ can is taken out from a refrigerator at $0^{\circ}C$. The atmospheric temperature is $25^{\circ}C$. If $t_1$ is the time taken to heat from $0^{\circ}C$ to $5^{\circ}C$ and $t_2$ is the time taken to heat from $10^{\circ}C$ to $15^{\circ}C$,then:

$A$ body takes $10 \, \text{minutes}$ to cool from $60 \, ^\circ\text{C}$ to $50 \, ^\circ\text{C}$. The temperature of the surroundings is constant at $25 \, ^\circ\text{C}$. Then, the temperature of the body after the next $10 \, \text{minutes}$ will be approximately ....... $^\circ\text{C}$

$A$ body cools from $70^{\circ} C$ to $40^{\circ} C$ in $5 \text{ min}$. Calculate the time it takes to cool from $60^{\circ} C$ to $40^{\circ} C$. The temperature of the surrounding is $20^{\circ} C$. (in $\text{ min}$)

According to Newton's law of cooling,the rate of cooling of a body is directly proportional to the ........

$A$ sphere,a cube,and a thin circular plate,all of the same material and same mass,are initially heated to the same high temperature and allowed to cool down under similar conditions. Then,the

Vedclass Test Series

Exam Paper Generator

Online Exam Module