A person makes a quantity of iced tea by mixing 500g of hot tea(c=4190J/(Kg.k) with an equal mass of ice(T=0c, L=333KJ/Kg). assume that mixture has negligible energy exchange with environment. If tea's initial temperature is 90c, then what is the temperature of mixture at the time of thermal equilibrim?

The heat absorbed by the ice in melting and rising to equilibrium temperature equals the heat lost by the rest of the water. Let T be the final temperature.

0.5kg*4.190(90 - T) = 0.5kg*(L + 4.190T)

The 0.5 kg cancels out since the masses are equal. You know what L is; solve for T.

4.190(90-T) = 333 + 4190T
2*4.190T = 377.1 -333 = 44.1
T = 5.3C

thank u so much drwls

To determine the temperature of the mixture at thermal equilibrium, we can consider the energy gained by the ice and the energy lost by the tea until they reach the same temperature.

First, let's calculate the energy gained by the ice to reach the final temperature:

Energy gained by ice (Q_ice) = mass of ice × specific latent heat of fusion
Q_ice = (500g) × (333 kJ/kg)
Q_ice = 166,500 J

Next, let's calculate the energy lost by the tea to reach the final temperature:

Energy lost by tea (Q_tea) = mass of tea × specific heat capacity of tea × change in temperature
Q_tea = (500g) × (4190 J/(kg·K)) × (90°C - T_final)

Since the energy gained by the ice is equal to the energy lost by the tea (assuming no energy exchange with the environment), we can set up an equation:

166,500 J = (500g) × (4190 J/(kg·K)) × (90°C - T_final)

Simplifying the equation:

166,500 J = 500g × 4190 J/(kg·K) × 90°C - T_final × 500g × 4190 J/(kg·K)
166,500 J = 1,885,500 J - T_final × 2,095,000 J/(kg·K)
T_final × 2,095,000 J/(kg·K) = 1,719,000 J
T_final = 1,719,000 J / 2,095,000 J/(kg·K)

T_final ≈ 0.82°C

Therefore, at thermal equilibrium, the temperature of the mixture will be approximately 0.82°C.

To find the temperature of the mixture at thermal equilibrium, we need to calculate the heat transferred between the tea and the ice.

First, let's calculate the heat absorbed by the hot tea to reach thermal equilibrium. We can use the formula:

Q = mcΔT

Where:
Q is the amount of heat transferred.
m is the mass of the hot tea.
c is the specific heat capacity of the hot tea.
ΔT is the change in temperature.

In this case, the mass of the hot tea is 500g, the specific heat capacity is 4190 J/(kg·K), and the change in temperature is (90°C - Tf), where Tf is the final temperature of the mixture.

So, the heat absorbed by the hot tea is:
Q1 = (0.5 kg) × (4190 J/(kg·K)) × (90°C - Tf)

Now, let's calculate the heat released by the ice to reach thermal equilibrium. We can use the formula:

Q = mL

Where:
Q is the amount of heat transferred.
m is the mass of the ice.
L is the latent heat of fusion for ice.

In this case, the mass of the ice is also 500g, and the latent heat of fusion for ice is 333 kJ/kg.

Converting the latent heat from kJ to J:
L = 333 kJ/kg × 1000 J/kJ = 333000 J/kg

So, the heat released by the ice is:
Q2 = (0.5 kg) × (333000 J/kg)

Since the total heat transferred is conserved, the values of Q1 and Q2 must be equal. Therefore, we can equate them:

Q1 = Q2

(0.5 kg) × (4190 J/(kg·K)) × (90°C - Tf) = (0.5 kg) × (333000 J/kg)

Now, we can solve the equation to find Tf:

(90°C - Tf) = (333000 J/kg) / (4190 J/(kg·K))

Simplifying:
90°C - Tf = 79.47 K

Rearranging the equation to solve for Tf:
Tf = 90°C - 79.47 K

Tf = 10.53 °C

Therefore, the temperature of the mixture at thermal equilibrium is approximately 10.53°C.