Question

x gram of water at 40 degrees celsius is mixed with 4 grams of water at 90 degrees celsius the final temperature of the water is 50

Answer 1

Answer:

since it is given that 50 gm water at 20 ⁰ C and 50 gm of water at 40⁰ C are mixed.  Since the masses of the liquid at different temperatures are same, the answer is very easy and simple :  average of 20⁰C and 40⁰C.  that is:  30⁰C.

Explanation:

final temperature of the mixture =  

    = [ m1 * T1 + m2 * T2 ] / (m1 + m2)

    = [ 50 gm * 20⁰ C + 50 gm * 40⁰C ]  / (50+50)  

    = 3,000 / 100 = 30⁰C  

another way using specific heats :  

  let the final temperature be = T ⁰C

  Amount of heat given out by the hot water = m * s * (40⁰C - T)

          = 50 gm * s* (40 -T)

  Amount of heat taken in by the cold water = m * s * (T - 20⁰C)

      = 50 gm * s * (T - 20 )  

  As the amounts are equal, because the heat is transferred from hot water to the cold water without any loss of heat to any surroundings,

          50 * s * (40 -T) = 50 gm * s  * (T-20)  

                40 - T = T - 20

            2 T = 60    => T = 30⁰C