1kg of water at 10degree Celsius is added to 10 kg of water at 50 degree Celsius. What will be the temperature when it reaches thermal equilibrium?
Answers
When 1 kg of water at 10 degree Celsius is added to 10 kg of water at 50 degree Celsius, the final temperature it attains is 44.5 degree celsius
Explanation:
1 kg of water was at 10° C
Assume that the final temperature of water after addition would be T° C.
Thus, T< 30°C.
The heat that is emitted by 10 kg of water at 50° C when it decreases T°C is calculated as = (mass) (Δt) (Cp)
Where, mass refers to the amount of water, i.e., 10 kg = 10000 g
Δt is the difference in the temperatures of water
= 10000 g × 1 calorie/g/°C × (50- T)° C =
= 10000 x 50 – 10000 x T cals
= 500000 – 10000 T cals .......................(1)
On the other hand, the heat that is acquired when 1 Kg of water at 10° C rises to T° = (mass) (Δt) (Cp)
= 1000 g × 1 calorie/g/°C × (T -10)° C
= 1000 T - 10,000 cals ............................ (2)
Heat emitted = Heat acquired
Hence, after noting Eqs 1 and 2;
1000 T – 10000 = 500000 – 10000 T
11000 T = 490000
T = 44.5 ° C
When 1 kg of water at 10 degree Celsius is added to 10 kg of water at 50 degree Celsius, the final temperature it attains is 44.5 degree celsius