The time taken for a calorimeter containing 7 | vedclass

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

Question

(B) According to Newton's law of cooling, the rate of cooling is proportional to the heat lost per unit time. Assuming the rate of heat loss $(dQ/dt)$

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(B) According to Newton's law of cooling, the rate of cooling is proportional to the heat lost per unit time. Assuming the rate of heat loss $(dQ/dt)$ is constant for the same temperature range:Heat lost $Q = (w + m) C_V \Delta T$where $w$ is the water equivalent of the calorimeter, $m$ is the mass of water, $C_V$ is the specific heat of water, and $\Delta T = 62^{\circ} C - 58^{\circ} C = 4^{\circ} C$.Since the rate of cooling is constant, the time taken $t \propto Q$.Case $I$: $t_1 = 9 \ 	ext{minutes}$, $m_1 = 75 \ g$$9 \propto (w + 75) C_V 	imes 4^{\circ} \quad \dots (i)$Case $II$: $t_2 = 12 \ 	ext{minutes}$, $m_2 = 105 \ g$$12 \propto (w + 105) C_V 	imes 4^{\circ} \quad \dots (ii)$Dividing equation $(i)$ by equation $(ii)$:$\frac{9}{12} = \frac{(w + 75) C_V 	imes 4^{\circ}}{(w + 105) C_V 	imes 4^{\circ}}$$\frac{3}{4} = \frac{w + 75}{w + 105}$$3(w + 105) = 4(w + 75)$$3w + 315 = 4w + 300$$w = 315 - 300 = 15 \ g$Thus, the water equivalent of the calorimeter is $15 \ g$.

Similar Questions

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

The catalyst and promoter respectively used in the Haber's process of industrial synthesis of ammonia are

The locus of a point such that the sum of its distances from the points $(0, 2)$ and $(0, -2)$ is $6$,is

Which artery is absent in a frog?

Vedclass Test Series

Exam Paper Generator

Online Exam Module