Question

1 kg of cold water at $5^{o}C$ is added to a container of 5 kg of hot water at ${65}^{o}C$. What is the final temperature of the water when it arrives at thermal equilibrium?

• A. ${10}^{o}C$
• B. ${15}^{o}C$
• C. ${35}^{o}C$
• D. ${55}^{o}C$
• E. ${60}^{o}C$

Answer 1

The correct option is D ${55}^{o}C$

Let mass of hot water $m_1=5kg$ ,

mass of cold water $m_2=1kg$ ,

temperature of hot water $=t_1={65}^{o}C$ ,

temperature of cold water $=t_2=5^{o}C$ ,

and $t=$ final temperature of both waters after thermal equilibrium

According to the principle of mixture ,

Heat lost = Heat gained

$m_{1}c(t-t_1)=m_{2}c(t_2-t)$

$5c(65-t)=1c(t-5)$

or $325-5t=t-5$

or $t=330/6={55}^{o}C$