Final answer:
To calculate the final temperature when hot water is poured into a glass cup, you can use the principle of conservation of energy. The final temperature when 200g of hot water at 95°C is poured into a cup with a mass of 150g initially at 15°C is approximately -40.48°C.
Step-by-step explanation:
To calculate the final temperature when hot water is poured into a glass cup, you can use the principle of conservation of energy, specifically the equation for heat transfer: Q = mcΔT. Q represents the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature. In this case, the initial temperature of the water is 95°C and the initial temperature of the cup is 15°C.
First, calculate the heat transferred from the hot water to the cup:
Q1 = mcΔT1
Q1 = (200g)(840 J/(g°C))(15°C - 95°C)
Q1 = -240,000 J
Next, calculate the heat transferred from the hot water to the cup:
Q2 = mcΔT2
Q2 = (150g)(840 J/(g°C))(15°C - t)
Q2 = 1260t - 189,000 J
Since the heat transferred from the hot water to the cup is equal to the heat transferred from the cup to the cold water, set Q1 equal to Q2:
-240,000 J = 1260t - 189,000 J
Solve for t:
t = (-240,000 J + 189,000 J) / 1260 J/°C
t = -51,000 J / 1260 J/°C
t ≈ -40.48°C
Therefore, the final temperature when 200g of hot water at 95°C is poured into a cup with a mass of 150g initially at 15°C is approximately -40.48°C.