Correct option is C
Given:
Initial water: 10 L at 15°C
Added water: x L at 50°C
Final mixture temperature: 40°C
No heat loss (heat gained = heat lost).
Concept Used:
The principle of heat exchange states:
Heat gained by cooler water = Heat lost by hotter water
The heat gained or lost by a substance is given by:
Q = m × c × ΔT
where:
m = mass (or volume in this case, since density of water is 1 kg/L)
c = specific heat (same for water, so it cancels out)
ΔT = change in temperature
Thus, we set up the equation:
(Mass of cold water) × (Temp increase) = (Mass of hot water) × (Temp decrease)
Solution:
Heat gained by cold water (10 L at 15°C):
10 × (40 - 15) = 10 × 25 = 250
Heat lost by hot water (x L at 50°C):
x × (50 - 40) = x × 10 = 10x
Setting heat gained = heat lost:
250 = 10x
Solving for x:
x = 250 / 10 = 25 L
Final Answer:
(C) 25 L
