Answer:
The final temperature is 111.66°C
Explanation:
The given conditions :-
i) Well insulated means no heat loss.
ii) Rigid vessels means volume remains same.
iii) Initial temperature ( T₁ ) = 40°C. = 273 + 40 = 313 K
iv ) Mass of water in vessel = 3 kg.
v) current drawn by resistor ( i ) = 10 ampere.
vi) Voltage applied ( V ) = 50 volts.
vii) The time for which resistor operating ( t ) = 30 minute = 30 * 60 = 1800 seconds.
Now we have to calculate heat developed by resistor in vessel.
Q = V * i * t = 50 * 10 * 1800 = 900,000 J = 900 KJ.
Since it is a rigid container so the work done is zero.
Q = du ( du - change in internal energy)
Q = m * C * dT ( C = 4.186 KJ/KgK )
Q = 3 * 4.186 * (T₂ - T₁ )
900 = 12.558 * ( T₂ - 313 )
T₂ - 313 = 71.6674
T₂ = 384.6674 K
T = 384.6674 - 273 = 111.66°C
So the final temperature is 111.66°C.
