Question

If we mix $1$kg of ice at $0^{o}C$ with $1$kg of steam at ${100}^{o}C.$ The final temperature of the mixture is

• A. ${15}^{o}C$
• B. ${50}^{o}C$
• C. ${100}^{o}C$
• D. None of these

Answer 1

The correct option is B ${50}^{o}C$

If we mix mass of $1kg$ of ice at temperature $=0°C$ with $1kg$ steam at temperature $=100°C$

Let, Final temperature of the mixture $t°C$

Solution

According to law of calorimetry

the absorptive heat by ice $=$ emitted heat by steam

$H_1=H_2$

$m_1{s}_2{t}_1=m_2{s}_2{t}_2$

where $m_1=$ mass of the ice $=1kg$

$m_2=$ mass of the steam$1kg$

$s_1=$ specific heat of ice$=2.108times{10}^{3}J/kgK$

$s_2=$ Specific heat of the steam $=2.010\times {10}^{3}J/kgK$

$2.108\times (t-0°)=2.010\times (100-t)t-0=\frac{2.010}{2.108}(100-t)t=0.99(100-t)t=49.8°C=50°C$