Question

A mass of 50 gram of water in a closed vessel with surroundings at a constant temperature takes 2 minutes to cool from 30 degree Celsius to 25 degree Celsius. Another liquid in analytical vessel with identical surroundings takes the same time to cool from 30 degree Celsius to 25 degree Celsius. Specific heat of liquid is ?

• A. 12 kilo calories per kg
• B. 17 kilo calories per kg
• C. 13 kilo calories per kg
• D. none

Answer 1

The correct option is D none

$\text{Solution}:$

As the surrounding is identical, vessel is identical time taken to cool both water and liquid ( from ${30}^{0}C$ to ${25}^{0}C$, Q is same 2 minutes ),

$\therefore {\left(\frac{dQ}{dT}\right)}_{water}={\left(\frac{dQ}{dt}\right)}_{liquid}$

or,$\frac{(m_w{C}_w+W)\Delta T}{t}=\frac{(m_l{C}_l+W)\Delta T}{t}$

(W = water equivalent of the vessel)

or, $m_w{C}_w=m_l{C}_l$

$\therefore$ Specific heat of liquid,

$C_l$ =$\frac{m_w{C}_w}{m_l}$=$\frac{50\times 1}{100}=0.5kcal/kg$

$\text{Hence D is the correct option}$