When water of mass70g and temperature 50^(@)Cis added to water of mass 30g, the maximum temperature of the mixutre is found to be 41^(@)C. Find the temperature of water of mass 30g before hot water was added to it.

When water of mass70g and temperature 50^(@)Cis added to water of mass

1.	When water of mass70g and temperature 50^(@)Cis added to water of mass 30g, the maximum temperature of the mixutre is found to be 41^(@)C. Find the temperature of water of mass 30g before hot water was added to it.
Answer» Solution :Data : `m_(1) = 70` g , `T_(1) = 50^(@)C , m_(2)= 30 g , T = 41^(@)C , T_(2)` = ? According to the principle of heat EXCHANGE ,heat LOST by hot water = heat gained by COLD water ` therefore m_(1)c (T_(1) - T) = m_(2) c (T - T_(2))` `therefore m_1T_(1) - m_1 T = m_(2) T - m_(2) T_(2)` `therefore m_(2) T_(2) = (m_(1) + m_(2)) T - m_(1) T_(1)` `therefore T_(2)= ((m_(1) + m_2) T - m_(1) T_1)/(m_(2))` `= ((70 g + 30 g ) 41^(@) C - 70 g xx 50^(@)C)/(30 g )` = `((100 xx 41 - 70 xx 50)/(30)) ""^(@)C` `= ((410 - 350)/(3)) ""^(@) C = (60)/(3) ""^(@)C = 20 ""^(@)C` This is the REQUIRED temperature .