Question

5 kg of water at 10°C is added to 10 kg of water at 40°C. Neglecting heat capacity of vessel and other losses, the equilibrium temperature will be(a) 30°C(b) 25°C(c) 35°C(d) 33°C

Answer 1

Answer:

A) 30°C

Explanation:

Using, conservation of energy which will be in the form of heat energy is given by - Q = mcΔT

Where, m is the mass, c is the specific heat capacity .

Let m1 = 5 kg  m2 = 10 kg

T1 = 10° C

T2 = 40° C

T3 = final temperature.

The energy of the 5 kg of water is:

Q1 = m1×c×T1 = (5 kg)×c×(10 C) = 50c J

Q2 = m2×c×T2 = (10 kg)×c×(40 C) = 400c J

After mixing, the energy is dispersed along 15 kg of water. The final energy becomes:

Q3 = (m1+m2)×c×T3 = 15cT

Conservation of energy allows -

Q1 + Q2 = Q3

m1×T1 + m2×T2 = (m1+m2)×T3

T3 = (m1×T1 + m2×T2)/(m1+m2)

T3 = 30 C

Thus, the equilibrium temperature will be 30°C