Question

A calorimeter of mass $0.2kg$ and specific heat $900J/kg-K$. Containing $0.5kg$ of a liquid of specific heat $2400J/kg-K$. Its temperature falls from ${60}^{\circ }C$ to ${55}^{\circ }C$ in one minute. The rate of cooling is

• A. $5j/s$
• B. $100j/s$
• C. $15j/s$
• D. $115j/s$

Answer 1

The correct option is D $115j/s$

Mass of the calorimeter $m_c=0.2kg$,

Specific heat of calorimeter
$c_c=900\frac{J}{kg-K}$

Mass of the liquid $m_l=0.5kg$
specific heat of liquid

$c_l=2400\frac{J}{kg-K}$

${\theta }_1={60}^{\circ }C$,

${\theta }_2={55}^{\circ }C$, $t=60sec$

Rate of cooling (here it is rate of loss of heat)

$\left|\frac{dQ}{dt}\right|=(mc+W)\frac{d\theta }{dt}$

$=(m_l{c}_l+m_c{c}_c)\frac{d\theta }{dt}$

$\frac{dQ}{dt}=(0.5\times 2400+0.2\times 900\left(\frac{60-50}{60}\right))$

$115J/sec$